1.05 g of an unknown gas at 47 °C and 1.05 atm is stored in a 2.25-L flask.
Density of the gas= 0.47g/L
What is the molar mass of the gas?
To find the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of the gas
R = Ideal Gas Constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 47 °C + 273.15
T(K) = 320.15 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (1.05 atm) * (2.25 L) / (0.0821 L·atm/mol·K) * (320.15 K)
n = 0.0745 mol
Next, we can calculate the molar mass (M) of the gas by dividing the mass of the gas (in grams) by the number of moles:
M = mass / moles
Given that the density of the gas is 0.47 g/L, we can calculate the mass of the gas:
mass = density * volume
mass = 0.47 g/L * 2.25 L
mass = 1.0575 g
Now, we can substitute the values into the equation to find the molar mass:
M = 1.0575 g / 0.0745 mol
M ≈ 14.18 g/mol
Therefore, the molar mass of the gas is approximately 14.18 g/mol.
To find the molar mass of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 47 + 273.15
T(K) = 320.15 K
Now, we can rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT
Substituting the known values into the equation:
n = (1.05 atm) * (2.25 L) / (0.0821 L·atm/(mol·K)) * (320.15 K)
n = 0.0783 mol
Now, we can calculate the molar mass using the given mass and number of moles:
Molar mass (g/mol) = Mass (g) / Number of moles (mol)
Molar mass (g/mol) = 1.05 g / 0.0783 mol
Molar mass (g/mol) ≈ 13.38 g/mol
Therefore, the molar mass of the gas is approximately 13.38 g/mol.