If 0.823g of an unknown gas occupies a volume of 702.0 mL at 38.9 deg. Celsius, and 726.2 mm Hg pressure, what is the molar mass of the gas? (pressure has already been corrected for water vapor pressure)
To find the molar mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 38.9 + 273.15
T(K) = 312.05 K
Next, convert the given pressure from mm Hg to atm:
P(atm) = P(mmHg) / 760
P(atm) = 726.2 / 760
P(atm) = 0.9555 atm
Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (0.9555 atm) * (0.7020 L) / (0.0821 L·atm/(mol·K) * 312.05 K)
Now, calculate the value of n using the given values:
n ≈ 0.0284 mol
Finally, to find the molar mass (M) of the gas, divide the mass of the gas (0.823g) by the number of moles (n):
M = mass / n
M ≈ 0.823 g / 0.0284 mol
M ≈ 28.98 g/mol
Therefore, the molar mass of the gas is approximately 28.98 g/mol.