Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 300 cm3, the pressure is 180 kPa, and the pressure is increasing at a rate of 30 kPa/min. At what rate is the volume decreasing at this instant?

Answers

Answer 1

Answer:

The gas is decreasing at a rate of 50 cubic centimeters per minute.

Explanation:

The Boyle's Law is represented by the following expression:

[tex]P\cdot V = k[/tex] (1)

Where:

[tex]P[/tex] - Pressure, in kilopascals.

[tex]V[/tex] - Volume, in cubic centimeters.

[tex]k[/tex] - Proportionality constant, in kilopascal-cubic centimeters.

By definitions of rate of change and implicit differentiation, we derive the following differential equation:

[tex]\dot P \cdot V + P\cdot \dot V = 0[/tex] (2)

Where:

[tex]\dot P[/tex] - Rate of change of the pressure, in kilopascals per minute.

[tex]\dot V[/tex] - Rate of change of the volume, in cubic centimeters per minute.

Then, we clear the rate of change of the volume within (2):

[tex]P\cdot \dot V = -\dot P\cdot V[/tex]

[tex]\dot V = -\left(\frac{\dot P}{P} \right) \cdot V[/tex]

If we know that [tex]P = 180\,kPa[/tex], [tex]\dot P = 30\,\frac{kPa}{min}[/tex] and [tex]V = 300\,cm^{3}[/tex], then the rate of change of the volume is:

[tex]\dot V = -\left(\frac{\dot P}{P} \right) \cdot V[/tex]

[tex]\dot V = -50\,\frac{cm^{3}}{min}[/tex]

The gas is decreasing at a rate of 50 cubic centimeters per minute.


Related Questions

At what temperature (in K) does NH₃ have a density of 0.812 g/L at 1.17 atm?

Answers

Answer:

The temperature is "298.51 K".

Explanation:

The given values are:

Density of ammonia,

d = 0.812 g/L

Pressure,

P = 1.17 atm

Mass:

M = [tex]NH_3[/tex]

   = [tex]14+ 1\times 3[/tex]

   = [tex]17[/tex]

As we know,

⇒ [tex]PV=nRT[/tex]

∴  [tex]T=\frac{PV}{nR}[/tex]

       [tex]=\frac{PV}{\frac{W}{M}\times R }[/tex]

       [tex]=\frac{PVM}{W\times R}[/tex]

By putting the value of "W", get

       [tex]=\frac{PVM}{V\times d\times R}[/tex]

       [tex]=\frac{P\times M}{d\times R}[/tex]

On substituting the values in the above equation, we get

       [tex]=\frac{1.17\times 17}{0.812\times 0.08205}[/tex]

       [tex]=\frac{19.89}{0.06699}[/tex]

       [tex]=298.51 \ K[/tex]

Answer:

299

Explanation:

Or 298.51 to be exact!

Volume and moles are __________ related. This relationship can be calculated by using ___________ Law.

indirectly; Boyle’s
directly; Boyle’s
indirectly; Charles’
directly; Charles’
indirectly; Avogadro’s
directly; Avogadro’s

Answers

Answer:

The correct answer is - directly; Avogadro’s.

Explanation:

At the same temperature and pressure, gases of the same or equal volume have the same number of molecules. The relation between the moles of the gases and the volume of the gases are indirectly proportional to one another at the same temperature and pressure. This law is called Avogadro's law. In the case of an ideal gas of a particular mass has the volume and moles are directly proportional.

Thus, the correct answer is - directly; Avogadro’s.

When one gram of liquid water at its boiling point is changed into water vapor
1.
334 J/g is gained from the surrounding environment
2.
334 J/g is released into the surrounding environment
3
2260 J/g is gained from the surrounding environment
4
2260 J/g is released into the surrounding environment

Answers

Answer: 2260 J/g is gained from the surrounding environment

When one gram of liquid water at its boiling point is changed into water vapor, 2260 J/g of energy is gained from the surrounding environment.

What is heat of vaporization?

Heat of vaporization is the amount of heat that is required by any body during their transition process from liquid state to vapor state, at a particular temperature i.e. no change in temperature during whole process.

During the transition of one gram of liquid water into water vapor at its boiling point of 100°C, 2260 J/g energy is absorbed by the water for the formation of vapor.

Hence, option (3) is correct.

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What’a the answer!!?

Answers

Answer:

2,1,2

1,2,1,1

the answer

If only one sperm cell is needed to fertilize an egg, why are males capable of producing so many sperm cells?

Answers

Males are capable of producing so many sperm cells because of the fact that even unprotected intercourse doesn’t always result in pregnancy. There are so many sperm cells to increase the chances of fertilizing the egg.

How many grams of nitrogen dioxide are required to produce 260 grams of nitrogen monoxide? 3NO2 + H20 → 2HNO3 + NO

Answers

Answer:

1196 g

Explanation:

N= 14 O= 16

every 3 moles of NO2 gives one mole of NO

So, 3[14 + (2×16)] = 138 grams of NO2

gives : 14+16 = 30 grams of NO

NO2 NO

138 30

? 260

Therefore, 260 × 138 ÷ 30 = 1196 g of NO2 are required

Your friend the archaeologist, who studies the ancient human past, has asked you to find a numerical date for some hominid artifacts found buried by ash from a volcanic eruption. To do this, you can use carbon-14 dating, which has a half-life of 5,730 years, or uranium-238, which has a half-life of 4.5 billion years. Based on their half-lives, which isotopic dating system will give your friend the most accurate numerical age

Answers

Answer:

I think it the carbon 14 which is a half life of 5730 because in 4.5billion years ago I don't think any human being existed on earth I'm not sure I hope that I helped you and good luck .

Carbon-14 dating will be used to find a numerical date for some hominid artifacts found buried by ash from a volcanic eruption.

What is carbon dating?

Radiocarbon dating also known as carbon dating or carbon-14 dating.

It is a method for establishing the age of an organic thing using the properties of radiocarbon, a radioactive carbon isotope.

Willard Libby created the approach in the late 1940s.

Thus, Carbon -14 dating will give your friend the most accurate numerical age.

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Need the answer please

Answers

i think A, I might be wrong though sorry

What is the name of the variable that changes by itself in an experiment?

Answers

Answer:

the independent variable (sometimes known as the manipulated variable )

Explanation:

is the variable whose change isn't affected by any other variable in the experiment

The frequency of a wave can be calculated by dividing the speed of a wave by its wavelength. Calculate the frequency of a radio wave having a speed of 300,000,000 m/s and a wavelength of 0.00056 m.

Answers

Answer:

snovd vosb r

Explanation:

Question 18 of 20
Which statement explains why a chemical equation must be balanced?
A. It must show how each chemical formula is written to accurately
represent each substance.
B. It must show that coefficients and subscripts can be used in
chemical formulas.
O C. It must show that the mass of each element involved is conserved
by a chemical reaction.
O D. It must show the reactants and products on the correct sides of
the reaction arrow.
SUBMIT

Answers

Answer:

d.It must show the reactants and products on the correct sides of

the reaction arrow

Explanation:

hope it helps

Calculate the pH and percent ionization of a HC2H3O2 solution with a concentration of 0.500 M. (Ka = 1.8 x10-5)

Answers

Answer:

I can not see the file

Explanation:

_______ prohibits and punishes certain conduct for the benefit of society.

Answers

Answer:

animal

Explanation:

follow and make brainliest

Please help I have no idea where to start

Answers

Answer:

Download Ptable, it will show all of the elements, and you can click on them, and it will show all the information you need about them!

Explanation:

I hope this helps!!!!!

Find out the atomic symbols by looking it up and then find it on the table. The second picture is labeled so you know what the different numbers mean! Hope that’s helpful :)

The empirical formula for compound is P2O5. The molar mass of the compound is 283.89g. What is the molecular formula?

Answers

Answer:

P4O10

Explanation:

(P2O5)n=283.89

62+80=283.89

142n=283.89

n=2

P2O10

The empirical and molecular formula are related by the formula, molecular formula=2×empirical formula ,meaning double the atoms present in empirical formula,hence molecular formula is P₄O₁₀.

What is empirical formula?

Empirical formula of a compound is defined as the simplest whole number ratio of atoms which are present in a compound.It does not make any mention of the arrangement of atoms or the number of atoms. The empirical formula gives information about the ratio of number of atoms which are present in a compound.

Molecular formula is determined from the empirical formula by dividing the molar mass of a compound by the empirical formula mass. The resultant which should be a whole number or very close to the whole number , then the subscripts are multiplied by the whole number to get the molecular formula.

For the compound P₂O₅ the subscripts of phosphorous and oxygen are multiplied by 2 and hence the molecular formula P₄O₁₀.

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A gas has an initial pressure of 2065 mmHg and temperature of 416 K. What is
the new pressure in atm if the temperature is cooled to 382 K?

Answers

Answer:

1896 mmHg

Explanation:

P1/T1 = P2/T2

P1 = 2065 mmHg

T1 = 416 K

P2 = ?

T2 = 382 K

Solve for P2 --> P2 = P1T2/T1

P2 = (2065 mmHg)(382 K) / (416 K) = 1896 mmHg

Why it is true to say that calcium carbonate has both ionic and covalent bonds?​

Answers

Answer:

Calcium carbonate is an ionically bonded compound.

Covalent Bond: This bond is formed because atoms share a pair of electrons through an orbital.

Which set of coefficients would be needed to balance the chemical equation below?

Answers

Answer:

2Zn2+3O2 ----> 2ZnO+2SO2

Explanation:

Balance Chemical Equations, will give brainiest.

Answers

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1) 2KCIO3=2kci+3o2

2)CH4 + 2O2 → CO2 + 2H2O

3)  2HCl + Ca(OH)2 → CaCl2 + 2H2O

I hope this helped!

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- Zack Slocum

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Please if you just want point TELL ME I can’t fail this.

Match the environmental stresses to what would happen in the chemical reaction. Think through the path from the carbon cycle - how CO2
CO2is removed from the atmosphere and stored in sinks and then how CO2
CO2is released from sinks and/or produced. Loss of carbon sinks, like trees

Decrease in shellfish due to overfishing

Decrease the number of farms

Increase in Earth's temperature

Decrease in number of cars burning gas

Answers

Answer:

here you go. I took the test :)

Explanation:

Wht is fluorine more chemically reactive than nitrogen

Answers

for many reasons fluorine is mor reactive than nitrogen

1: F is more electronegative atom than N

2: F just needs an electron and N needs 3 electrons to reach noble gases electron configuration

4: F2 bond is weaker than N2 bond

HELP FAST 100 PTS Calculate the amount of heat needed to lower the temperature of 50.0g of ice from -40 °C to -100 °C.

Answers

It would be -20 I think not sure

Answer:

[tex]\Large \boxed{\sf -6000 \ J}[/tex]

Explanation:

Use formula

[tex]\displaystyle \sf Heat \ (J)=mass \ (kg) \times specific \ heat \ capacity \ (Jkg^{-1}\°C^{-1}) \times change \ in \ temperature \ (\°C)[/tex]

Specific heat capacity of ice is 2,000 J/(kg °C)

Substitute the values in formula and evaluate

[tex]\displaystyle \sf Heat \ (J)=0.05 \ kg \times 2000 \ Jkg^{-1}\°C^{-1} \times (-100\°C-(-40 \°C))[/tex]

[tex]Q=0.05 \times 2000 \times (-100-(-40)) =-6000[/tex]

According to the Brinsted -Lowry. what is an acid ? what is a base ? ​

Answers

Answer:

According to the Brønsted definition, an acid is a substance capable of donating a proton, and a base is a substance capable of accepting a proton. ... The species giving up the proton is HCl, an acid. The species accepting the proton is water, the base. The species Cl- is the conjugate base of HCl.

What are the two products of an acid base neutralization reaction?

Answers

Answer:

Neutralization reactions occur when two reactants, an acid and a base, combine to form the products salt and water.

Explanation:

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Answer: Water and NaCl is always formed

Explanation:

I hope this helped!

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Any groups present on a benzene ring can impact the success and regioselectivity of an electrophilic aromatic substitution. Determine which group from the list best fits each activation and directing description.

Strongly deactivating meta- director __________
Moderately deactivating meta- director ________
Strongly activating ortho-/para- director _________
Weakly deactivating ortho-/para- director _________
Weakly activating ortho-/para- director ________

Answers

Answer:

Explanation:

In electrophilic aromatic substitution, the substituent(s) that favors electrophilic attack is said to be ortho or para to the substituent. Meta directors are deactivators. Altogether, these directors have an integral role to play in the success and regioselectivity of electrophilic aromatic substitution reactions.

From the information given: The;

Strongly deactivating meta- director  ⇒ NO₂ (nitro group)

Moderately deactivating meta- director  ⇒ CN (cyano group)

Strongly activating ortho-/para- director ⇒ OH (hydroxy; group)

Weakly deactivating ortho-/para- director ⇒ -X (halide group)

Weakly activating ortho-/para- director ⇒ - Ph  (phenyl group)

Ortho and para substituents favors the electrophilic substitution reaction and meta substituents are deactivators.

What is regioselectivity ?

Regioselectivity of any reaction tells about the preferred side over another side of the reaction to success.

Ortho or para substituents on the benzene ring will increase the chances of electrophilic aromatic substitution by increase the s electrons on the ring. While the meta directors are deactivators, they have an integral role to play in the success and regioselectivity of electrophilic aromatic substitution reactions.

Strongly deactivating meta director nitro group.

Moderately deactivating meta director cyano group.

Strongly activating ortho/para director hydroxy group.

Weakly deactivating ortho/para director halide group.

Weakly activating ortho/para director phenyl group.

Hence, from the above discussion it is clear that Ortho and para substituents favors the electrophilic substitution reaction and meta substituents are deactivators.

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Unit 4.2 quiz chemistry

Answers

Additional oxygen

Explanation : H2O is two hydrogens and one oxygen not 2 hydrogens two oxygens

Explain clearly in 2 ways each in which a soap and a detergent are similar and different.​

Answers

Explanation:

the soap is the product made from a detergent

1. Chlorofluorocarbons (CFCs) are of interest because of their ability to destroy ozone molecules. A carbon-chlorine bon din the CFC molecule can be broken by sunlight, leaving a highly reactive free radical which then goes on to destroy the surrounding ozone molecules. The energy of a C-Cl bond is 328 kJ/mole. Calculate the wavelength of light needed to break a bond in a single molecule. In which region of the spectrum (infrared, visible, UV) does this wavelength fall

Answers

Answer:

See explanation

Explanation:

Energy of the photon (E) = 328 * 10^3/6.02 * 10^23 = 5.45 * 10^-19 J

Recall that E = hc/λ

h = Plank's constant = 6.36 * 10^-34 Js

c = speed of light = 3 * 10^8 m/s

λ = ??

λ = hc/E

λ = 6.36 * 10^-34 * 3 * 10^8/5.45 * 10^-19

λ = 3.5 * 10^-7 m

This falls into the UV region of the spectrum

1) This rock is made out of cooled magma.

A) Igneous

B) Sedimentary

C) Metamorphic

D) Sandstone


2) This type of rock is made through the processes of heat and pressure.

A) Igneous

B) Sedimentary

C) Metamorphic

D) Sand



3) Sandstone is a sedimentary rock. How does sandstone form?



A) It melted and cooled.

B) It broke into sediment and then compacted.

C) It was heated and put under pressure.

D) Rocks don’t form; they stay as they are.



4) What type of rock can be broken down into sediment through weathering?

A) Igneous

B) Sedimentary

C) Metamorphic

D) All types of rocks



5) How does rock from a mountain turn into small pieces of rock?

A) Wind and rain break the rock into small pieces.

B) Earthquakes and natural disasters break the rock.

C) The sun's rays break the rock.

D) Everything breaks into pieces if you leave it out.



6) Can igneous rock underneath Earth’s outer layer change into sedimentary rock?

A) Yes, but it must be subducted first.

B) Yes, but it must be weathered first.

C) Yes, but it must be uplifted first.

D) No, igneous rock can never become sedimentary.



7) This energy source creates magma, which is melted rock that will turn into igneous rock.

A) Sun

B) Air

C) Earth's Interior

D) Water


8) This energy source helps create weather, which creates sediment to form sedimentary rocks.

A) Air

B) Sun

C) Water

D) Earth's Interior


9) What is the difference between magma and lava?


A) Magma is very hot, lava is cool.

B) Magma is molten rock within the earth; lava is molten rock on the earth's surface.

C) Magma is molten rock on the earth's surface; lava is molten rock within the earth.

D) Magma is cool, lava is very hot.

Answers

1. a) Igneous.

2. c) Metamorphic.

3. b) It broke into sediment and then compacted.

4. d) All types of rocks.

5. a) Wind and rain break down the rock into small pieces.

6. a) Yes, but it should be subtuced first.

7. c) Earth's interior.

8. c) Water.

9. b) Magma is molten rock within the Earth; lava is molten rock on the Earth's surface.

Express
as
ordinary numbers.
3 x 10^0=

Answers

any number to the power of zero is equal to 1
so 10^0=1 and 3 x 1 = 3 !
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