Answer :
The molar mass of the compound in grams per mole (g/mol) is 0.3166 g/mol.
To find the molar mass of a gaseous compound, we can use the ideal gas law equation:
PV = nRT
Where
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant,
T is the temperature
First, let's convert the density of the gas from grams per liter (g/L) to moles per liter (mol/L). To do this, we need to divide the given density by the molar mass of the compound.
The density of the gas is given as 1.57 g/L. Let's assume the molar mass of the compound is M g/mol. Therefore, we have:
1.57 g/L = (1 mol/M g) / (1 L)
Now, let's rearrange the equation to solve for the molar mass (M):
M = (1 mol) / (1.57 g/L)
Next, we can use the ideal gas law equation to find the number of moles (n) of the gas. The pressure (P) is given as 1.64 atm, the temperature (T) is given as 29.0°C, and the ideal gas constant (R) is 0.0821 L·atm/(mol·K).
PV = nRT
(1.64 atm)(V) = n(0.0821 L·atm/(mol·K))(29.0 + 273.15 K)
Simplifying the equation, we have:
1.64 atm(V) = n(0.0821 L·atm/(mol·K))(302.15 K)
Now, let's substitute the value of n from the previous step:
1.64 atm(V) = [(1 mol) / (1.57 g/L)](0.0821 L·atm/(mol·K))(302.15 K)
Simplifying further, we get:
1.64 atm(V) = 0.5193 L·atm/g(V)
Finally, we can solve for V:
V = (1.64 atm) / (0.5193 atm/g)
V ≈ 3.158 g/mol
Now that we have the value of V, we can substitute it back into the equation for molar mass (M):
M = (1 mol) / V
M = (1 mol) / (3.158 g/mol)
≈ 0.3166 g/mol
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