Answer:
The problem of energy exchange between waves and particles, which leads to energization of the latter, in an unstable plasma typical of the radiation belts. The ongoing Van Allen Probes space mission brought this problem among the most discussed in space physics. A free energy which is present in an unstable plasma provides the indispensable condition for energy transfer from lower energy particles to higher-energy particles via resonant wave-particle interaction. This process is studied in detail by the example of electron interactions with whistler mode wave packets originated from lightning-induced emission. We emphasize that in an unstable plasma, the energy source for electron energization is the energy of other particles, rather than the wave energy as is often assumed. The way by which the energy is transferred from lower energy to higher-energy particles includes two processes that operate concurrently, in the same space-time domain, or sequentially, in different space-time domains, in which a given wave packet is located. In the first process, one group of resonant particles gives the energy to the wave. The second process consists in wave absorption by another group of resonant particles, whose energy therefore increases. We argue that this mechanism represents an efficient means of electron energization in the radiation belts.
Explanation:
Fun facts:
In the process of energy transfer between two groups of particles both processes operate simultaneously, and if the lower energy part of plasma distribution gives energy to the wave while the higher‐energy part absorbs the wave enrgy, then the wave‐mediated energy transfer from lower energy particles to higher‐energy ...
Ammonium sulfate (NH4)2SO4 is made by reacting 25.0 L of 3.0 mol/L H2SO4 with 3.1× 103 L of NH3 at a pressure of 0.68 atm and a temperature of 298 K according to the following reaction .
NH3(g) + H2SO4(aq) → (NH4)2SO4 (aq)
How many grams of ammonium sulfate are produced?
Answer: The mass of [tex](NH_4)_2SO_4[/tex] produced is 9910.5 g
Explanation:
For [tex]H_2SO_4[/tex]:Molarity is calculated by using the equation:
[tex]\text{Molarity}=\frac{\text{Moles}}{\text{Volume}}[/tex] ......(1)
Molarity of [tex]H_2SO_4[/tex] = 3.0 M
Volume of solution = 25.0 L
Putting values in equation 1, we get:
[tex]\text{Moles of }H_2SO_4=(3.0mol/L\times 25.0L)=75mol[/tex]
For [tex]NH_3[/tex]:The ideal gas equation is given as:
[tex]PV=nRT[/tex] .......(2)
where,
P = pressure of the gas = 0.68 atm
V = volume of gas = [tex]3.1\times 10^3L[/tex]
n = number of moles of gas = ? moles
R = Gas constant = 0.0821 L.atm/mol.K
T = temperature of the gas = 298 K
Putting values in equation 2, we get:
[tex]0.68atm\times 3.1\times 10^3L=n\times 0.0821L.atm/mol.K\times 298K\\\\n=\frac{0.68\times 3.1\times 10^3}{0.0821\times 298}=86.16mol[/tex]
For the given chemical equation:
[tex]NH_3(g)+H_2SO_4(aq)\rightarrow (NH_4)_2SO_4(aq)[/tex]
By stoichiometry of the reaction:
If 1 mole of [tex]H_2SO_4[/tex] reacts with 1 mole of [tex]NH_3[/tex]
So, 75 moles of [tex]H_2SO_4[/tex] will react with = [tex]\frac{1}{1}\times 75=75mol[/tex] of [tex]NH_3[/tex]
As the given amount of [tex]NH_3[/tex] is more than the required amount. Thus, it is present in excess and is considered as an excess reagent
Thus, [tex]H_2SO_4[/tex] is considered a limiting reagent because it limits the formation of the product.
By the stoichiometry of the reaction:
If 1 mole of [tex]H_2SO_4[/tex] produces 1 mole of [tex](NH_4)_2SO_4[/tex]
So, 75 moles of [tex]H_2SO_4[/tex] will produce = [tex]\frac{1}{1}\times 75=75mol[/tex] of [tex](NH_4)_2SO_4[/tex]
The number of moles is defined as the ratio of the mass of a substance to its molar mass. The equation used is:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
We know, molar mass of [tex](NH_4)_2SO_4[/tex] = 132.14 g/mol
Putting values in above equation, we get:
[tex]\text{Mass of }(NH_4)_2SO_4=(75mol\times 132.14g/mol)=9910.5g[/tex]
Hence, the mass of [tex](NH_4)_2SO_4[/tex] produced is 9910.5 g
Label each formula and name pair as correct or incorrect.
Formula Name Correct/Incorrect
Aluminum tribromide
Sulfur dioxide
Beryllium hydride
Magnesium(II) oxide
Copper(II) oxide
Calcium sulfate
Nitric acid
Answer:
Aluminum tribromide: AlBr₃, however, it should be just aluminum bromide.
Sulfur dioxide: SO₂.
Beryllium hydride: BeH₂
Magnesium(II) oxide: MgO; however the roman numeral is not used in Mg as it just has one oxidation number.
Copper(II) oxide: CuO.
Calcium sulfate: CaSO₄
Nitric acid: HNO₃.
Explanation:
Hello there!
In this case, it seems that the formulas were not given, however, we can write the correct one for each given compound according to the widely used nomenclature rules as shown below:
Aluminum tribromide: AlBr₃, however, it should be just aluminum bromide.
Sulfur dioxide: SO₂.
Beryllium hydride: BeH₂
Magnesium(II) oxide: MgO; however the roman numeral is not used in Mg as it just has one oxidation number.
Copper(II) oxide: CuO.
Calcium sulfate: CaSO₄
Nitric acid: HNO₃.
Regards!
When taking a measurement with a pH meter, keep the instrument in the ______________ until it is needed. Rinse the pH meter with ______________ and gently pat dry. Place the meter in the sample solution, and record the measurement when the pH __________
Answer:
Storage solution; deionized water; stabilizes.
Explanation:
The pH scale measures the concentration of hydrogen ions in acidic and alkaline solutions.
In chemistry, it literally means power of hydrogen ions and it is a measure of the molar concentration of hydrogen ions in a particular solution, thus specifying the acidity, neutrality or basicity of chemical solutions.
Mathematically, the pH of a solution is given by;
[tex] pH = -log_{10}(H^{+}) [/tex]
Hence, a solution with a pH of 7 is neutral. Also, a solution with a pH below 7 is acidic but basic (alkaline) if it's pH is above 7.
A pH meter can be defined as a scientific instrument or device designed and developed for the measurement of the hydrogen-ion concentration in water-based solutions, in order to determine their level of acidity or alkanility.
When using a pH meter to take a measurement, you should keep it in a storage solution until it is needed. Also, a deionized water should be used to rinse the pH meter and gently pat dry.
Furthermore, the pH meter should be placed in a given sample solution and a reading of the measurement taken when the pH of the solution stabilizes.
Which of the following is not generally a characteristic of metal?
Ductility
O
Malleability
High melting point
Low boiling point
What are the characteristics of an acid-base neutralization reaction?
The weak ionization constant (Ka)
for HCN is equal to:
Answer:
Ka = [H⁺] × [CN⁻] / [HCN]
Explanation:
Cyanhydric acid is a weak acid, according to the following equation:
HCN(aq) ⇄ H⁺(aq) + CN⁻(aq)
The acid ionization constant (Ka) is equal to the product of the concentrations of the ions raised to the stoichiometric coefficients divided by the concentration of the undissociated acid raised to its stoichiometric coefficient.
Ka for HCN is:
Ka = [H⁺] × [CN⁻] / [HCN]
The formula for europium oxide is Eu203. On the basis of this information, the formula for the chlorate of europium would be expected to be
Answer:
Eu(ClO3)3
Explanation:
The chlorate ion is written as follows, ClO⁻ ₃. We can see from this that the ion is univalent.
From the formula, Eu203, it is easy to see that the europium ion is trivalent.
Hence, when a compound is formed between the europium ion and chlorate ion, the compound will be written as Eu(ClO3)3.
This is so because, when ionic compounds are formed, there is an exchange of valence between the ions in the compound. This gives the final formula of the ionic substance.
Between energy and life which one comes first answer with scientific reason
Explanation:
While the sun is an excellent source of energy, not all forms of life can utilize the sun's energy directly. This lesson describes how plants transform the sun's energy into potential energy stored in sugar, how living organisms utilize energy in sugar to perform work, and how the relationship between photosynthesis and cellular respiration is necessary for life.
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Which of the following choices is a source of groundwater pollution?
O sewage
very warm water
O silt
O All of these choices are correct.
Answer:
very warm water consuving
Based on your knowledge of factors affecting the rate of reaction, why is there a danger of explosions in places such as flour mills and coal mines where there are large quantities of powdered, combustible materials?
Answer:
See Explanation
Explanation:
Rate of reaction refers to how quickly or slowly a reaction proceeds. The rate of reaction depends on certain factors.
Two among the factors that affect the rate of reaction are the concentration of reactants and the surface area of reactants.
The more the concentration of reactants, the faster the rate of reactants because there is a high possibility of collision between reactants. Also, the higher the surface area of reactants, the greater the rate of reaction.
In flour mills and coal mines where there is a large amount (concentration) of combustible materials and the particles are powdered (high surface area), there is a greater risk of explosion due to a high rate of reaction owing to a combination of the two factors discussed above.
Compare the solubility of silver iodide in each of the following aqueous solutions:
a. 0.10 M AgCH3COO
b. 0.10 M NaI
c. 0.10 M KCH3COO
d. 0.10 M NH4NO3
1. More soluble than in pure water.
2. Similar solubility as in pure water.
3. Less soluble than in pure water.
Answer:
Compare the solubility of silver iodide in each of the following aqueous solutions:
a. 0.10 M AgCH3COO
b. 0.10 M NaI
c. 0.10 M KCH3COO
d. 0.10 M NH4NO3
1. More soluble than in pure water.
2. Similar solubility as in pure water.
3. Less soluble than in pure water.
Explanation:
This can be explained based on common ion effect.
According to common ion effect the solubility of a sparingly soluble salt decreases further in a solution which has a common ion to it.
The solubility of AgI(s) silver iodide in water is shown below:
[tex]AgI(s) <=> Ag^{+}(aq)+I^{-}(aq)\\[/tex]
a. a. 0.10 M AgCH3COO has a common ion Ag+ with AgI.
So, AgI is less soluble than in pure water in this solution.
b. 0.10 M NaI has a common ion I- with AgI.
So, AgI is less soluble than in pure water in this solution.
c. 0.10 M KCH3COO:
This solution has no common ion with AgI.
So, AgI has similar solubility as in pure water.
d. 0.10 M NH4NO3:
In this solution, AgI can be more soluble than in pure water.
which of group of organism has the least biomass?which has the least energy
Answer:
The answer is consumers
Answer:
Consumers are the group of organisms that has the least biomass and energy.
After mixing the solutions in a separatory funnel, the stopper should be ______ and the liquid should be _______ and the layers allowed to separate. When you get close to the interface between the layers, ______ the funnel and turn over _______ heat up until the first layer is collected get eye level with to collect the second layer. _______
Answer:
Hence,
1) removed
2) drained through the stopcock
3) get eye level with
4) slow the draining
5) switch to a new flask
Explanation:
After mixing the solutions in a separatory funnel, the stopper should be removed and the liquid should be drained through the stopcock, and the layers allowed to separate. When you get close to the interface between the layers, get eye level with the funnel and turn over to slow the draining heat up until the first layer is collected. Switch to a new flask get eye level with it to collect the second layer.
A scientist collects a sample that has 2.00 × 1014 molecules of carbon dioxide gas.How many grams is this, given that the molar mass of CO2 is 44.01 g/mol?
Answer:
1.46 × 10⁻⁸ g
Explanation:
Step 1: Given data
Molecules of CO₂: 2.00 × 10¹⁴ molecules
Step 2: Convert molecules to moles
We need a conversion factor: Avogadro's number. There are 6.02 × 10²³ molecules in 1 mole of molecules.
2.00 × 10¹⁴ molecules × 1 mol/6.02 × 10²³ = 3.32 × 10⁻¹⁰ mol
Step 3: Convert moles to mass
We need a conversion factor: the molar mass. The molar mass of CO₂is 44.01 g/mol.
3.32 × 10⁻¹⁰ mol × 44.01 g/mol = 1.46 × 10⁻⁸ g
The oxidation number of nitrogen in NO2 is:
a. 1.
b. 2.
c. 3.
d. 4.
e. 5.
f. None of the above.
Answer:
Option D. 4
Explanation:
The oxidation number of nitrogen (N) in NO₂ can be obtained as follow:
Oxidation number of O = –2
Oxidation number of N =?
N + 2O = 0
N + 2(–2) = 0
N – 4 = 0
Collect like terms
N = 0 + 4
N = +4
Thus, the oxidation number of nitrogen (N) in NO₂ is +4
What are the labeled structures
Answer:
a
Explanation:
A recipe calls for 1/4 cup of butter. One ounce (oz) of butter is equivalent to 2 tablespoons (T), and there are 8 oz of butter in 1 cup. Which of the following statements correctly interpret the information provided?
a. The information provided gives the conversion factor 8oz/2T.
b. The information provided gives the conversion factor 8oz/1 cup.
c. The recipe requires 64 T of butter.
d. The recipe requires 4T of butter.
Answer:
D
Explanation:
8oz=1cup
Xoz=1/4cup
cross multiply
Xoz=8×1/4=2
2oz=1/4cup
1oz=2T
2oz=x
cross multiply
×=2×2=4T
The cup of butter, number of tablespoons and ounces of butter are all in direct proportion with one another. The interpretation of the information provided is:
(b). The information provided gives the conversion factor 8oz/1 cup.
Given that:
[tex]1\ recipe = \frac{1}{4}\ cup[/tex]
[tex]1\ oz = 2T[/tex]
[tex]8\ oz = 1\ cup[/tex]
Multiply both sides of [tex]1\ oz = 2T[/tex] by 8
[tex]8 \times 1oz = 8 \times 2T[/tex]
[tex]8 oz = 16T[/tex]
Substitute 8oz for 1 cup in: [tex]1\ recipe = \frac{1}{4}\ cup[/tex]
[tex]1\ recipe = \frac{1}{4} \times 8oz[/tex]
Substitute [tex]8 oz = 16T[/tex]
[tex]1\ recipe = \frac{1}{4} \times 16T[/tex]
[tex]1\ recipe = 4T[/tex]
The interpretations are as follows:
[tex]1\ recipe = 4T[/tex] means that 1 recipe requires 4T of butter [tex]8\ oz = 1\ cup[/tex] means that the information provided gives a conversion of 8oz/1 cupHence, (b) is correct
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Select the statement(s) that describe the characteristics of transition metals. a. Transition metals have partially filled d subshells. b. Transition metals give rise to cations that have completely filled d subshells. c. Group 2B elements are not transition metals because they neither have nor readily acquire partially filled d orbitals.
Answer: The correct option is A,
--> a.) Transition metals have partially filled d subshells.
Explanation:
Transition elements are all metals of economic importance. They are found in the d- lock of the periodic table between group 2 and 3. They occupy three rows, with ten elements in each row. The term 'transition metals' refers only to an element which has PARTIALLY filled d orbitals. Typical example of transition metals include iron (Fe).
They have partially filled 3d orbitals which are responsible for the special properties of the metals. These include:
--> Physical properties: the transition metals have high boiling and melting points. They are hard, dense and lustrous. They are also good conductors of heat and electricity.
--> Chemical reactivity: In the s- block and p-block, the chemical properties of the elements in the same period vary, often quite markedly, from left to right. This does not happen with the transition metals because electrons are added progressively to the inner d-orbitals.
--> Variable oxidation states: they have variable oxidation states because 3d electrons are available for bond formation.
Some chemical bonds are considered molecules while others are considered compounds.
Explain what the difference is and provide one example for each.
Molecule is the general term used to describe any atoms that are connected by chemical bonds. Every combination of atoms is a molecule. A compound is a molecule made of atoms from different elements. All compounds are molecules, but not all molecules are compounds.
One example of a molecule is [tex]Cl_2[/tex] (chlorine).
Examples of a compound is NaCl (sodium chloride) or [tex]H_2O\\[/tex] (water)
5-Analysis of a 12.04-g sample of a liquid compound composed of carbon, hydrogen, and nitrogen showed it to contain 7.34 g C, 1.85 g H, and 2.85 g N. What is the percent composition of this compound
Answer:
%C = 60.9%; %H = 15.4%; %N = 23.7%
Explanation:
Step 1: Given data
Mass of the sample (m): 12.04 gMass of Carbon (mC): 7.34 gMass of Hydrogen (mH): 1.85 gMass of Nitrogen (mN): 2.85 gStep 2: Calculate the percent composition of this compound
To calculate the percent by mass of any element (E), we will use the following expression.
%E = mE/m × 100%
%C = 7.34 g/12.04 g × 100% = 60.9%
%H = 1.85 g/12.04 g × 100% = 15.4%
%N = 2.85 g/12.04 g × 100% = 23.7%
Hydrofluoric acid is used in the preparation of numerous pharmaceuticals (e.g., Prozac) and industrial materials (e.g., Teflon). It can be produced by the reaction of hydrogen and fluorine gases. Starting with initial concentrations of 1.69 M for H2 and 1.69 M for F2, what would be the equilibrium concentration of HF? The equilibrium constant for the reaction Kc = 115.
a. 2.85 M.
b. 4.00 M.
c. 0.85 M.
d. 3.37 M.
e. 1.69 M.
Answer:
the equilibrium concentration of HF is 2.85 M
Option a) 2.85 M is the correct answer.
Explanation:
Given the data in the question;
H₂ + F₂ ⇄ 2HF
I 1.69 M 1.69 M 0
C -x -x +2x
E 1.69-x 1.69-x +2x
given that Kc = 115
Kc = [ HF ]² / [H₂][F₂]
we substitute
115 = [ 2x ]² / [ 1.69-x ][ 1.69-x ]
lets find the square root of both sides
10.7238 = 2x / [ 1.69-x ]
10.7238[ 1.69-x ] = 2x
18.123222 - 10.7238x = 2x
2x + 10.7238x = 18.123222
12.7238x = 18.123222
x = 18.123222 / 12.7238
x = 1.424356
Hence, equilibrium concentration of HF = 2x
that is;
HF = 2 × 1.424356
HF = 2.8487 ≈ 2.85 M
Therefore, the equilibrium concentration of HF is 2.85 M
Option a) 2.85 M is the correct answer.
Water is considered to be a diatomic molecule because it composed of two different atoms. True or false?
Answer:
false
Explanation:
False, water is a polyatomic molecule made up of two atoms of oxygen and 1 atom of hydrogen.
Explanation:
The monoatomic molecule is composed of a single atom of an element.For example: Helium(He) , argon(Ar) etc.The diatomic molecule is composed of two atoms of the same or different elements.For example: hydrochloric acid (HCl), sodium chloride (NaCl) etc.The polyatomic molecule is composed of three or more than three atoms of the same or different elements.For example: water ([tex]H_2O[/tex]), sodium hydroxide(NaOH) etc.So, from this, we can conclude that water is a polyatomic molecule made up of two atoms of oxygen and 1 atom of hydrogen.
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Which is the balanced version of the half-reaction below?
H2S → S+H+
Answer:
C. [tex]H_2S\rightarrow S+2H^++2e^-[/tex]
Explanation:
Hello there!
In this case, according to the given chemical reaction, it turns out possible to realize there is one sulfur atom on each side of the chemical equation but two hydrogen atoms on the left and one on the right, which means the latter must be balanced in agreement to the law of conservation of mass.
In such a way, by setting a 2 on H⁺, the reaction will be balanced:
[tex]H_2S\rightarrow S+2H^+[/tex]
Now, we count the transfer electrons for sulfur from -2 to 0 as 2e⁻ on the right, which will match with the option C.
[tex]H_2S\rightarrow S+2H^++2e^-[/tex]
Regards!
Name the following compound: Cuzs
O sulfur copperide (ll)
O sulfur copperide (1)
O copper(I) sulfide
copper(ll) sulfide
Answer:
THE ANSWER IS: copper(I) sulfide.
hope this helped <3
Explanation:
0-17, an isotope of oxygen, has 9 neutrons. The
of oxygen is 8.
isotope number
atomic number
mass number
atomic mass
Answer:
atomic number
Explanation:
The mass number (A) of an element is obtained by summing the number of neutrons and protons (nucleons) in the atom of that element. However, the proton number of an element is its atomic number (Z). Hence, it can be said that:
mass number = no. of neutrons + atomic number/number of protons.
According to this question, an isotope of oxygen is said to have a mass number of 17. If the neutron number of this isotope is given as 9, then this means that its ATOMIC NUMBER or no. of protons of that isotope is (17 - 9) = 8.
Answer:
atomic number
Explanation:
Anew fictitious element was discovered. It is a metal named jolmium, J,and it has three valence electrons. If it combineswith iodine it forms jolmium iodide. Answer the following questions.a.Is this compound ionic or covalent
a. Is this compound ionic or covalent?
b. What is the formula of Jolmium iodide?
c. What is the charge on the metal J in this compound?
d. Explain how you know that is the charge?
Answer:
A new fictitious element was discovered.
It is a metal named jolmium, J, and it has three valence electrons.
If it combines with iodine it forms jolmium iodide. Answer the following questions.
a.Is this compound ionic or covalent
b. What is the formula of Jolmium iodide?
c. What is the charge on the metal J in this compound?
d. Explain how you know that is the charge?
Explanation:
It is given the element jolmium J is a metal with three valence electrons.
Since metals are highly electropositive, they lose electrons easily and form cations (Ions with a positive charge).
[tex]J^{3+}[/tex] ion will be formed.
b) The formula of jolmium iodide is shown below:
[tex]J^{+3} I^{-1}\\The formula becomes:\\JI_{3}[/tex]
a) The compound is ionic in nature.
Since the compound formed between a metal atom and a nonmetal atom will take place by transfer of electrons.
Hence, it is ionic in nature.
c) The charge on the metal J in this compound is +3.
d) Given J has three valence electrons.
That means it can lose three electrons to form a bond.
So, its valency is three.
Sodium azide, NaN3, the explosive compound found in automobile air bags, decomposes according to the following equation: 2NaN3(s)right arrow 2Na(s) + 3N2(g)
What mass of NaN3 is required to provide the nitrogen needed to inflate an 80.0-L bag to a pressure of 1.3 atm at 27 degree C? What is the density of the gas under these conditions?
Answer:
1.9 × 10² g NaN₃
1.5 g/L
Explanation:
Step 1: Write the balanced decomposition equation
2 NaN₃(s) ⇒ 2 Na(s) + 3 N₂(g)
Step 2: Calculate the moles of N₂ formed
N₂ occupies a 80.0 L bag at 1.3 atm and 27 °C (300 K). We will calculate the moles of N₂ using the ideal gas equation.
P × V = n × R × T
n = P × V / R × T
n = 1.3 atm × 80.0 L / (0.0821 atm.L/mol.K) × 300 K = 4.2 mol
We can also calculate the mass of nitrogen using the molar mass (M) 28.01 g/mol.
4.2 mol × 28.01 g/mol = 1.2 × 10² g
Step 3: Calculate the mass of NaN₃ needed to form 1.2 × 10² g of N₂
The mass ratio of NaN₃ to N₂ is 130.02:84.03.
1.2 × 10² g N₂ × 130.02 g NaN₃/84.03 g N₂ = 1.9 × 10² g NaN₃
Step 4: Calculate the density of N₂
We will use the following expression.
ρ = P × M / R × T
ρ = 1.3 atm × 28.01 g/mol / (0.0821 atm.L/mol.K) × 300 K = 1.5 g/L
The compound magnesium nitrate has the formula Mg(NO3)2.
What is the relative formula mass of magnesium nitrate?
Explanation:
Answer
Open in answr app
Correct option is
C
148
1 atom of Mg=1x24=24
2 atom of N=2x14=28
6 atom of O=6x16=96
Total mass=148
Suppose a piece of silver jewelry contains 7.49x10^22 atoms of silver (Ag). how many moles of silver are in the jewelry?
Answer:
0.124 mol Ag
General Formulas and Concepts:
Atomic Structure
MolesStoichiometry
Using Dimensional AnalysisExplanation:
Step 1: Define
[Given] 7.49 × 10²² atoms Ag
[Solve] mol Ag
Step 2: Identify Conversions
Avogadro's Number - 6.022 × 10²³ atoms, molecules, formula units, etc.
Step 3: Convert
[DA] Set up: [tex]\displaystyle 7.49 \cdot 10^{22} \ atoms \ Ag(\frac{1 \ mol \ Ag}{6.022 \cdot 10^{23} \ atoms \ Ag})[/tex][DA] Divide [Cancel out units]: [tex]\displaystyle 0.124377 \ mol \ Ag[/tex]Step 4: Check
Follow sig fig rules and round. We are given 3 sig figs.
0.124377 mol Ag ≈ 0.124 mol Ag
Topic: AP Chemistry
Orthogonal vectors we use theorem for
Pythagoras
true
false