Calculate the density of xenon gas at a pressure of 749 mmHg
and a temperature of 38 ∘C
.
Express the density to three significant figures and include the appropriate units.
To calculate the density of xenon gas at a pressure of 749 mmHg and a temperature of 38 ∘C, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (749 mmHg)
V = volume (since we are calculating density, we can assume a volume of 1 L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (38 ∘C = 311 K)
Rearranging the equation to solve for density (d):
d = (P * M) / (R * T)
Where:
M = molar mass of xenon (131.29 g/mol)
Now substitute the values and calculate the density:
d = (749 mmHg * 131.29 g/mol) / (0.0821 L.atm/mol.K * 311 K)
d = (98395.21 g.mmHg) / (25.6071 L.mmHg/mol)
d = 3839.52 g/L
Therefore, the density of xenon gas at a pressure of 749 mmHg and a temperature of 38 ∘C is approximately 3839.52 g/L.