# A gas occupies #"67. cm"^3# at #9.38 × 10^4color(white)(l)"Pa"# and 22 °C. What is its volume at #10.6 × 10^5color(white)(l)"Pa"# and 29 °C?

##### 2 Answers

#### Explanation:

So, it's always a good idea to start by making a note of what information is being provided by the problem.

In your case, you know that the initial sample of gas

occupies a volume equal to#"67 cm"^3# has a temperature of#22^@"C"# has a pressure of#9.38 * 10^4"Pa"#

You then go on to change the temperature to

Notice that no mention of number of moles was made. This means that you can assume it to be **constant**. So, if you start from the ideal gas law equation, you can say that

#P_1 * V_1 = n * R * T_1 -># the initial state of the gas

and

#P_2 * V_2 = n * R * T_2 -># the final state of the gas

Since *constant*, and *universal gas constant*, you can rearrange these equations to isolate these two constant terms on one side

#(P_1 * V_1)/T_1 = n * R" "# and#" "(P_2 * V_2)/T_2 = n * R#

Notice that you have two expressions that are equal to the same value,

#(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2 -># the combined gas law equation

Now all you have to do is rearrange this to solve for

Look what happens if you divide both sides of the equation by

#P_1/P_2 * V_1/T_1 = (color(red)(cancel(color(black)(P_2))) * V_2)/(T_2 * color(red)(cancel(color(black)(P_2))))#

#P_1/P_2 * V_1/T_1 = V_2/T_2#

Now multiply both sides by

#P_1/P_2 * T_2/T_1 * V_1 = V_2/color(red)(cancel(color(black)(T_2))) * color(red)(cancel(color(black)(T_2)))#

Finally, you got

#V_2 = P_1/P_2 * T_2/T_1 * V_1#

Now plug in your values and solve for **do not** foget to convert the temperature from degrees Celsius to Kelvin!

#V_2 = (9.38 * 10^4color(red)(cancel(color(black)("Pa"))))/(10.6 * 10^5color(red)(cancel(color(black)("Pa")))) * ((273.15 + 29)color(red)(cancel(color(black)("K"))))/((273.15 + 22)color(red)(cancel(color(black)("K")))) * "67 cm"^3#

#V_2 = "6.0695 cm"^3#

You need to round this off to two sig figs, the number of sig figs you have for the initial volume of the gas

#V_2 = color(green)("6.1 cm"^3)#

The new volume will be

#### Explanation:

We use the Combined Gas Law equation,

Let's start by listing our given information.

Now we must rearrange the Combined Gas Law equation to get

We'll take it step by step.

**Step 1.** Multiply both sides by

**Step 2.** Divide both sides by

Now we insert the values into the equation.

**Check**: The temperature doesn't change much, but the pressure increases by about ten-fold.

The new volume should be about one-tenth of the original volume, or about