# Question ae6c9

Jun 18, 2015

The volume is equal to ${\text{910 cm}}^{3}$.

#### Explanation:

Since you didn't specify the pressure and tmperature at which the gas is kept, I'll assume that you're dealing with STP conditions.

STP conditions imply a pressure of 100 kPa and a temperature of 273.15 K. When these condtions are met, 1 mole of any ideal gas occupies exactly 22.7 L - this is known as the molar volume of a gas at STP.

So, if you know that 1 mole of any ideal gas occupies 22.7 L, the volume your gas occupies is equal to

0.040cancel("moles") * "22.7 L"/(1cancel("mole")) = "0.908 L"#

Since you need this value expressed in cubic centimeters and rounded to two sig figs, the number of sig figs you a gave for the moles of gas, the answer will be

$0.908 \cancel{{\text{L") * ("1000 cm"^3)/(1cancel("L")) = color(green)("910 cm}}^{3}}$

SIDE NOTE Many online sources and textbooks use a pressure of 1 atm and a temperature of 273.15 K for STP. Under these conditions, the molar volume of a gas at STP is 22.4 L.

If that's the value given to you, simply replace 22.7 with 22.4 in the calculation for volume.

If you're not at STP conditions, use the ideal gas law equation to solve for the volume of the gas.

$P V = n R T \implies V = \frac{n R T}{P}$