A sample of gas has a mass of 0.555 g. Its volume is 119 mL at a temperature of 90 degrees C and a pressure of 744 mmHg. What is the molar mass of the gas?
To find the molar mass of the gas, we need to use the ideal gas law equation. The ideal gas law is represented as follows:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/mol·K or 62.36 mmHg·L/mol·K)
T = temperature of the gas in Kelvin
First, let's convert the given values to appropriate units:
Mass: 0.555 g
Volume: 119 mL = 0.119 L
Temperature: 90 degrees C = 90 + 273.15 = 363.15 K
Pressure: 744 mmHg
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
Plugging in the given values:
n = (744 mmHg * 0.119 L) / (62.36 mmHg·L/mol·K * 363.15 K)
Simplifying:
n = 0.895 mol
Next, we can calculate the molar mass (M) using the formula:
M = mass / moles
Plugging in the given values:
M = 0.555 g / 0.895 mol
M = 0.62 g/mol
Therefore, the molar mass of the gas is 0.62 g/mol.
To calculate the molar mass of a gas, we need to use the Ideal Gas Law equation:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L·atm/mol·K for this calculation)
- T is the temperature of the gas in Kelvin
First, let's convert the given values to the correct units:
- Pressure: 744 mmHg = 0.981 atm (since 1 atm = 760 mmHg)
- Volume: 119 mL = 0.119 L (since 1 L = 1000 mL)
- Temperature: 90 degrees C = 363 K (since 0 degrees C = 273 K)
Now we can rearrange the equation to solve for the number of moles (n):
n = (PV) / (RT)
Substituting the values we have:
n = (0.981 atm) * (0.119 L) / ((0.0821 L·atm/mol·K) * (363 K))
Calculating this expression gives us the number of moles of the gas.
Next, to find the molar mass of the gas, we divide the mass of the gas by the number of moles:
Molar mass = mass / moles
Given that the mass of the gas is 0.555 g (converted from 0.555 g), we can divide this value by the number of moles calculated earlier to find the molar mass.