# Question 8b63a

Dec 1, 2014

You will need to use the ideal gas law to answer this question. The ideal gas law is given by the mathematical formula $\text{PV}$ = $\text{nRT}$, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. When using the gas laws, the temperature needs to be in Kelvins, which is done by adding 273 to the Celsius temperature. The gas constant R can be represented by different units, but in this problem $\text{R}$ = $\text{0.08206 L atm K"^(−1) "mol"^(−1)}$.

Given/Known:
$\text{P}$ = $\text{1.000 atm}$
$\text{V}$ = $\text{100. L}$
$\text{T}$ = $\text{1325 C}$ + $\text{273}$ = $\text{1598K}$
$\text{R}$ = "0.08206 L atm K"^(−1) "mol"^(−1)"#.

Unkown :
number of moles, n

Equation:
$\text{PV}$ = $\text{nRT}$

Solution:

Divide both sides of the equation by $\text{RT}$ to isolate $\text{n}$. Solve for $\text{n}$.

$\text{n}$ = $\text{PV"/"RT}$ = $\text{(1.000)(100.)""/(0.08206)(1598)}$ = $\text{0.763 mol}$ (rounded to three significant figures due to 100. having three significant figures.

The number of moles of a gas under the conditions given is $\text{0.763}$.