A gas occupies 100.0 mL at a pressure of 780 mm Hg. What is the volume of the gas when its pressure is increased to 880 mm Hg?

Answer 1

Ask what variables are involved and what the relationship there is between them. Here we are dealing with a gas experiencing changes in pressure and volume; their relationship is inversely proportional. We are assuming that we are dealing with an ideal gas. We are also assuming that there is no change in temperature or in the number of moles of gas. These are good assumptions since no other information is given about the gas.

First make a prediction: the pressure goes up so the volume should go down.

Use Boyle's Law: P₁V₁ = P₂V₂

Where V₁ = 100 ml, P₁ = 780 mm Hg and P₂ = 880 mm Hg.

Rearrange the equation to solve for V₂:

V₂ = P₁V₁ / P₂

and substitute: (note that no unit conversions are required)

V₂ = 780 mmHg*100mL/880 mmHg = 88.6 mL

The volume went down like we predicted.

Answer 2

Hey Pou,

This question is trying to assess your understanding of the ideal gas laws. The equation that we'd want to use is PV=nRT (where P=pressure (in atm), V=volume (in L), n=number of moles of gas, R= gas constant, and T=temperature in Kelvin).

So, what you are given is initial V=100mL and initial P=780mmHg.

In order to convert 100mL to L, we need to multiply 100mL by 1L/1000mL ---> 100mL * (1L/1000mL). This would give us .1L.

In order to convert 780mmHg to atm, we need to multiply 780mmHg by 1atm/760mmHg ---> 780mmHg * (1atm/760mmHg). This would give us 1.0263atm.

We do the same thing for P₂ and we get P₂=1.158atm.

Now that we have our given values with correct units, we can start plugging in values to the formula!

But before doing so, we can see that a derivation of ideal gas law can be used, since nRT is staying constant, and we are only changing the PV portion of the formula.

In this case, we can use Boyle's law to solve this problem. Boyles's law is a derivation of ideal gas law that says: P₁V₁=P₂V_{2 .}

So, 1.0263atm*0.1L=1.158atm * V₂

V₂=0.0886L

I hope this helps! Let me know if you'd like me to explain more :)