The density of an elemental gas is 1.7824 g/L at STP. What is the molar mass of the element?
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To find the molar mass of the element, we can use the ideal gas equation:
PV = nRT
Where:
P = pressure (at STP, it is 1 atm)
V = volume (given as 1 L)
n = number of moles
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (at STP, it is 273.15 K)
Rearranging the equation to solve for n:
n = PV / RT
Given that the density of the gas is 1.7824 g/L, we can convert this to moles using the molar mass (M) of the gas:
n = density / M
Combining these equations, we can solve for the molar mass:
M = density / (PV / RT)
Plugging in the values:
M = 1.7824 g/L / (1 atm * 1 L / mol * 0.0821 L·atm/mol·K * 273.15 K)
M = 1.7824 g/L / (0.0821 * 273.15 mol/K)
Calculating this gives us:
M ≈ 28.98 g/mol
Therefore, the molar mass of the element is approximately 28.98 g/mol.
To find the molar mass of the element, we need to know the density of the gas and its molar volume at STP.
STP (standard temperature and pressure) is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (atm).
Given that the density of the elemental gas at STP is 1.7824 g/L, we can use this information to calculate the molar mass.
The molar volume at STP is the volume occupied by one mole of gas at STP conditions, which is approximately 22.414 L/mol.
To calculate the molar mass, we can use the formula:
Molar mass = (Density x Molar volume) / 1000
Plugging in the given values:
Molar mass = (1.7824 g/L x 22.414 L/mol) / 1000
Molar mass = 0.04 g/mol
Therefore, the molar mass of the element is 0.04 g/mol.