To solve this problem, we can use the Ideal Gas Law, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas. The Ideal Gas Law is expressed as:
PV = nRT
where R is the gas constant.
R = 0.0821 L·atm/mol·K
We can rearrange this equation to solve for pressure:
P = nRT/V
where:
n = 0.500 mol (number of moles of N2 gas)
R = 0.0821 L·atm/mol·K (gas constant)
T = 298 K (temperature)
V = 10.0 L (volume)
Substituting the values:
P = (0.500 mol)(0.0821 L·atm/mol·K)(298 K)/(10.0 L)
P = 12.1 atm
Therefore, the pressure exerted by a 0.500 mol sample of N2 gas in a 10.0 L container at 298 K is 12.1 atm.