help me pls w this chemistry question

Question

A gas occupies 24 L at 273 K and 1.0 atm. What is the volume if the conditions change to 388 K and 3.0 atm?

Answer 1

Hi Sarah!

This is a Combined Gas Law question. The Combined Gas Law tells us how an ideal gas will change if we alter the pressure, volume, and/or temperature at a constant amount of moles. The equation is as follows:

P1V1 = P2V2

T1 T2

Where:

P1 is the initial pressure and P2 is the new pressure

V1 is the initial volume and V2 is the new volume

T1 is the initial temperature and T2 is the new temperature

Note that the temperature must be in Kelvin (so if it's in Celsius, convert by adding 273.15)

P1 and P2 must be in the same units

V1 and V2 must be in the same units

Now let's look at your problem!

1) Write down your givens:

V1 = 24 L V2 = ?

T1 = 273 K T2 = 388 K

P1 = 1.0 atm P2 = 3.0 atm

2) Make sure everything is in the correct units:

Temperature is in Kelvin? Check!

P1 and P2 have the same units? Check!

Since V1 is in liters, our V2 will also be in L.

3) Plug in and solve for V2:

P1V1 = P2V2

T1 T2

(1.0 atm)(24 L) = (3.0 atm) V2

273 K 388 K

Rearranging the above, we get:

V2 = (1.0 atm)(24 L)(388 K)

(273 K)(3.0 atm)

V2 = 11.36996 L

4) Use the correct significant figures and units:

When multiplying or dividing, we look for the least number of significant figures. Our volume and pressure values are given to us with 2 sig figs while our temperatures have 3 sig figs. Since 2 < 3, our final answer will have 2 significant figures.

Therefore, our final answer is 11 L

Hope this helps! :)

Answer 2

This question involves using the combined gas law P₁V₁/ T₁ = P₂V₂/ T₂

Identifying each parameter, you are solving for V₂

V₂ = P₁V₁T₂ / P₂T₁

= (1.00 atm x 24 L x 388 K) / (3 atm x 273 K) = 11 L

Note: 2 significant figures for the answer based on information given...

Answer 3

In order to solve this problem, we need to utilize the combined gas law.

P₁V₁/T₁ = P₂V₂/T₂

Where P stands for pressure, V is volume, and T is temperature in Kelvin.

Our initial conditions are: Our final conditions are:

P₁ = 1.0 atm P₂ = 3.0 atm

T₁ = 273 K T₂ = 388 K

V₁ = 24 L V₂ = ?

We are solving for the final pressure, V₂.

We start by rearranging the equation to isolate V₂.

To do this, we multiply both sides of the equation by T₂/P₂

T₂/P₂ * P₁V₁/T₁ = P₂V₂/T₂ * T₂/P₂

to get

P₁V₁T₂/T₁P₂ = P₂V₂T₂/T₂P₂

We cancel out the terms that are present in both the numerator and denominator.

P₁V₁T₂/T₁P₂ = P₂V₂T₂/T₂P₂

Leaving us with

P₁V₁T₂/T₁P₂ = T₂

Now all that's left is to substitute our known quantities (from above) and calculate our answer!

(1.0 atm * 24 L * 388 K)/(273 K * 3.0 atm) = V₂

V₂ = 11 L

So our answer is 11 L (rounded to 2 significant figures).