Gas X has a density of 2.60 g/L at STP. Determine the molar mass of
this gas.
1 mole of a gas occupies 22.4 L at STP.
Density = 2.50 g/L x 22.4 L = ?? grams.
To determine the molar mass of Gas X, we need to use the Ideal Gas Law equation, which states:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/K·mol)
T = temperature (in Kelvin)
At STP (Standard Temperature and Pressure), the conditions are defined as:
T = 273.15 K
P = 1 atm
First, let's rearrange the Ideal Gas Law equation to solve for the number of moles (n):
n = PV / RT
Since we have the density of Gas X, we can also relate density (d) to molar mass (M) using the formula:
d = (M/P) * (1/RT)
Rearranging this equation, we get:
M = d * P * (1/RT)
Now, substitute the values into the equation:
d = 2.60 g/L
P = 1 atm
R = 0.0821 L·atm/K·mol
T = 273.15 K
M = (2.60 g/L) * (1 atm) * (1/0.0821 L·atm/K·mol) * (1/273.15 K)
Simplifying the expression, we get:
M = 0.0963 g/mol
Therefore, the molar mass of Gas X is approximately 0.0963 g/mol.
To determine the molar mass of a gas, we need to use the ideal gas law, which relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas.
However, since we are given the density of the gas at standard temperature and pressure (STP), we can use the relationship between density, molar mass, and volume to find the molar mass.
The density (d) can be defined as the mass (m) of the gas divided by its volume (V):
d = m/V
In this case, the given density is 2.60 g/L. Let's assume we have 1 mole of gas (n = 1) and we know the molar mass (M) of the gas.
The mass (m) of 1 mole of gas is simply the molar mass (M) in grams:
m = M
Substituting these values into the density equation, we get:
2.60 g/L = M/1 L
To find the molar mass (M), we can multiply both sides of the equation by 1 L:
2.60 g/L * 1 L = M
Therefore, the molar mass of the gas is 2.60 g/mol.