# Question #9008a

##### 1 Answer

#### Explanation:

This is a pretty straightforward example of how the ideal gas law can be used to determine the number of moles of a gas when given the volume, temperature ,and pressure of the sample.

The ideal gas law equation looks like this

#color(blue)(PV = nRT)" "# , where

*universal gas constant*, usually given as

Now, an important thing to notice here is that the units given to you for the temperature, pressure, and volume of the gas **do not match** what is used for the universal gas constant,

More specifically, you have

- pressure in torr
#-># you need it in atm- volume in mililiters
#-># you need it in liters- temperature in degrees Celsius
#-># you need it in Kelvin

Keep this in mind when plugging in your values in the ideal gas law equation. Rearrange the equation to solve for

#PV = nRT implies n = (PV)/(RT)#

#n = (820.0/760color(red)(cancel(color(black)("atm"))) * 50.0 * 10^(-3)color(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 + 60.0)color(red)(cancel(color(black)("K"))))#

#n = "0.001975 moles Ar"#

To get the mass of argon, use its molar mass, which tells you what the mass of *one mole* of argon is

#0.001975color(red)(cancel(color(black)("moles Ar"))) * "39.948 g Ar"/(1color(red)(cancel(color(black)("mole Ar")))) = "0.078897 g Ar"#

Now, you need to round both values to three sig figs, the number of sig figs you have for the temperature and volume of the gas

#n = color(green)("0.00198 moles")" "# and#" "m = color(green)("0.0789 g")#

**Alternatively**, you can use the ideal gas law equation to solve directly for the mass of the gas.

You know that you can write the number of moles of a gas as the ratio between mass and molar mass

#n = m/M_"M"#

This means that you can write the ideal gas law equation as

#PV = overbrace(m/M_"M")^(color(blue)(=n))RT#

Rearranging to solve for #m will get you

#m = (PV)/(RT) * M_"M"#