# If 9.69 moles of an ideal gas has a pressure of 3.10 atm, and a volume of 64.51 L, what is the temperature of the sample?

##### 1 Answer

#### Answer:

#### Explanation:

All you have to do here is use the **ideal gas law equation**, which looks like this

#color(blue)(ul(color(black)(PV = nRT)))#

Here

#P# is the pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the sample#R# is theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof the gas

Rearrange the equation to solve for

#PV = nRT implies T = (PV)/(nR)#

Before plugging in your values, make sure that the units given to you **match** those used in the expression of the universal gas constant.

In this case, the volume is given in *liters* and the pressure in *atmospheres*, so you're good to go.

Plug in your values to find

#T = (3.10 color(red)(cancel(color(black)("atm"))) * 64.51 color(red)(cancel(color(black)("L"))))/(9.69 color(red)(cancel(color(black)("moles"))) * 0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * "K"))#

#color(darkgreen)(ul(color(black)(T = "251 K")))#

The answer is rounded to three **sig figs**.