An experiment shows that a 111ml gas sample has a mass of 0.161g at a pressure of 725mmHG and a temperature of 36degrees C.What is the molar mass of the gas?
Use PV = nRT and solve for n = number of mols of gas. Then n = grams/molar mass. You have n and grams, solve for molar mass. Remember T must be in kelvin.
To find the molar mass of the gas, we can use the ideal gas law, which is represented by the equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
In order to use the ideal gas law, we need to convert the given values to the appropriate units.
1. We need to convert the pressure from millimeters of mercury (mmHg) to atmospheres (atm). We know that 1 atm is equal to 760 mmHg, so:
Pressure (in atm) = 725 mmHg / 760 mmHg/atm
Pressure (in atm) = 0.954 atm
2. We need to convert the volume from milliliters (ml) to liters (L). Since 1 L is equal to 1000 ml, we can convert:
Volume (in L) = 111 ml / 1000 ml/L
Volume (in L) = 0.111 L
3. We need to convert the temperature from Celsius (°C) to Kelvin (K). We can convert using the following equation:
Temperature (in K) = Celsius temperature + 273.15
Temperature (in K) = 36°C + 273.15
Temperature (in K) = 309.15 K
Now we have all the values needed to solve the ideal gas law equation. Rearranging the equation to solve for n (number of moles), we have:
n = PV / RT
Substituting the known values:
n = (0.954 atm)(0.111 L) / (0.0821 L·atm/mol·K)(309.15 K)
n = 0.0103 mol
Finally, we can find the molar mass (M) of the gas by dividing the mass of the gas (0.161 g) by the number of moles (0.0103 mol):
Molar mass (M) = mass (g) / moles (mol)
M = 0.161 g / 0.0103 mol
M ≈ 15.63 g/mol
Therefore, the molar mass of the gas is approximately 15.63 g/mol.