# A 73.8 g sample of O2 gas at 0.0 oC and 5.065x10^4 Pa is compressed and heated until the volume is 3.26 L and the temperature is 27 oC. What is the final pressure in Pa? T= 273K and 300K i think u have to convert L to m^3?

##### 1 Answer

#### Answer:

#### Explanation:

Yes, you will need to do some unit conversions, but I think it'll be easier to just convert the pressure from *Pa* to *atm*.

The idea here is that the *amount of gas* remains **unchanged**, but that changing the volume and temperature of the sample will result in a change in *pressure*.

This means that you can use the combined gas law equation to help you find the new pressure of the sample.

#color(blue)((P_1V_1)/T_1 = (P_2V_2)/T_2)" "# , where

The two temperature of the gas must be expressed in Kelvin. So, rearrange the above equation to solve for

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

Before solving for **initial volume** of the sample,

#color(blue)(P_1V_1 = nRT_1 implies V_1 = (nRT_1)/P_1#

Use oxygen gas' molar mass to determine how many moles you have in the sample

#73.8color(red)(cancel(color(black)("g"))) * "1 mole O"_2/(32.0color(red)(cancel(color(black)("g")))) = "2.301 moles O"_2#

Now, you need to convert the initial pressure of the gas from *Pa* to *atm* by using the conversion factor

#"1 atm " = " 101325 Pa" = 1.101325 * 10^5"Pa"#

#5.065 * 10^4color(red)(cancel(color(black)("Pa"))) * "1 atm"/(1.01325 * 10^5color(red)(cancel(color(black)("Pa")))) = "0.4999 atm"#

Now plug in your values and solve for

#V = (2.301color(red)(cancel(color(black)("moles"))) * 0.0821 (color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 273.15color(red)(cancel(color(black)("K"))))/(0.4999color(red)(cancel(color(black)("atm")))) = "103.41 L"#

Now that you have all you need to find *Pa*, since you need the final pressure to be in *Pa* as well!

#P_2 = ( 103.41 color(red)(cancel(color(black)("L"))))/(3.26color(red)(cancel(color(black)("L")))) * ( 300.15color(red)(cancel(color(black)("K"))))/(273.15color(red)(cancel(color(black)("K")))) * 5.065 * 10^4"Pa"#

#P_2 = color(green)(1.8 * 10^6"Pa")#

The answer is rounded to two sig figs, the number of sig figs you have for the two temperatures of the gas.