# If 2.30 g occupies 0.870 L at 690 torr and 37 degrees C. How would you calculate the molar mass?

##### 1 Answer

#### Explanation:

To get the *molar mass* of the gas, which tells you what the mass of **one mole** of the gas is, you need to determine how many moles you have in that sample.

SInce you are given volume, pressure, and temperature, you can use the ideal gas law

#color(blue)(PV = nRT)#

to solve for

The *universal gas constant*,

#R = 0.082("atm" * "L")/("mol" * "K")#

which means that you will have to convert the pressure of the gas from *torr* to *atm* by using the conversion factor

#"1 atm " = " 760 torr"#

So, plug in your values and solve for

#n = (PV)/(RT)#

#n = (690/760color(red)(cancel(color(black)("atm"))) * 0.870color(red)(cancel(color(black)("L"))))/(0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 37)color(red)(cancel(color(black)("K")))) = "0.03106 moles"#

This means that the molar mass of the gas will be equal to

#color(blue)(M_"m" = m/n)#

#M_"m" = "2.30 g"/"0.03106 moles" = "74.05 g/mol"#

Rounded to two sig figs, the answer will be

#M_"m" = color(green)("74 g/mol")#

Here's another solved example