A quantity of gas weighing 7.10g at 741 torr and 44 degrees C occupies a volume of 5.40 L. What is its molar mass?
PV=nRT
solve for moles, n. then, molmass=mass/moles
To find the molar mass of the gas, we can use the ideal gas law:
PV = nRT
Where:
P = pressure = 741 torr
V = volume = 5.40 L
n = number of moles of gas
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin
First, let's convert the temperature from degrees Celsius to Kelvin using the equation:
T(K) = T(°C) + 273.15
T(K) = 44°C + 273.15 = 317.15 K
Now, we can rearrange the ideal gas law and solve for the number of moles (n) of gas:
n = PV / (RT)
n = (741 torr * 5.40 L) / (0.0821 L·atm/(mol·K) * 317.15 K)
n ≈ 0.18 mol
Next, we can calculate the molar mass (M) of the gas using the equation:
M = mass / n
M = 7.10 g / 0.18 mol
M ≈ 39.44 g/mol
Therefore, the molar mass of the gas is approximately 39.44 g/mol.
To find the molar mass of a gas, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure of the gas (in torr)
V is the volume of the gas (in liters)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K) or 62.36 L·torr/(mol·K))
T is the temperature of the gas (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin. We can do this by adding 273.15 to the Celsius temperature:
44°C + 273.15 = 317.15 K
Now, let's substitute the given values into the ideal gas law equation:
(741 torr)(5.40 L) = n(0.0821 L·atm/(mol·K))(317.15 K)
Simplifying the equation, we get:
4004.4 = n(26.08)
Next, solve for the number of moles (n):
n = 4004.4 / 26.08
n ≈ 153.43 moles
Lastly, calculate the molar mass (M) by dividing the mass of the gas (in grams) by the number of moles:
M = mass of gas / n
Given that the mass of the gas is 7.10g, we can substitute the values:
M = 7.10 g / 153.43 mol
M ≈ 0.046 g/mol
Therefore, the molar mass of the gas is approximately 0.046 g/mol.