A sample of gas has a mass of 0.550g . Its volume is 111mL at a temperature of 75∘C and a pressure of 763mmHg . Find molar mass of gas
Use PV = nRT and solve for n = number of mols of gas. Then n = grams/molar mass. YOu know n and grams, solve for molar mass.
To find the molar mass of a gas, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature in Kelvin
In this case, we have the volume (V = 111 mL = 0.111 L), temperature (T = 75°C = 75 + 273 = 348 K), and pressure (P = 763 mmHg).
To find the number of moles (n) of gas, we need to rearrange the equation to solve for n:
n = PV / RT
Now let's plug in the values:
n = (763 mmHg * 0.111 L) / (0.0821 L atm mol^−1 K^−1 * 348 K)
Note: We convert the units of pressure to atmospheres (1 atm = 760 mmHg) to match the units of the ideal gas constant.
Simplifying the calculation:
n = 0.0821 mol^-1 L atm^-1 * 0.111 L * 763 mmHg / (0.0821 L atm mol^−1 K^−1 * 348 K)
= 0.0909 mol
Now, we can find the molar mass (M) of the gas using the formula:
M = mass / n
Plugging in the given mass (0.550 g) and the calculated number of moles (0.0909 mol):
M = 0.550 g / 0.0909 mol
Calculating:
M ≈ 6.032 g/mol
Therefore, the molar mass of the gas is approximately 6.032 g/mol.