Answer:
0.00133 g/cm^3 or 28.97 g/mol.
Step-by-step explanation:
To solve the problem, we'll need to use the ideal gas law: PV = nRT
Where:
P = Pressure (we'll assume atmospheric pressure, since it's not specified in the problem)
V = Volume (1.05 x 10^3 cm^3)
n = moles of gas
R = Gas Constant (0.08206 L.atm/K.mol)
T = Temperature (25 + 273.15 K = 298.15 K)
First, let's find the mass of the gas alone:
Mass of gas = Mass of container + gas - Mass of container Mass of gas = 837.6 g - 836.2 g
Mass of gas = 1.4 g
Next, we need to find the number of moles of gas:
n = m/M
where: m = mass of gas (1.4 g) M = molar mass of the gas (unknown)
We don't know the molar mass of the gas yet, so let's rearrange the ideal gas law to solve for it:
M = m/ (n/V) RT
Substitute the values we know so far:
M = 1.4 g / [(n/V)RT]
We'll need to find n/V to substitute into the equation. This can be found using the density formula:
Density = mass/volume
Rearrange the formula to solve for n/V:
n/V = Density / Molar mass
Substitute the values we know:
Density = mass/volume = 1.4 g / 1.05 x 10^3 cm^3
Density = 0.00133 g/cm^3
Substitute this value into the formula to find n/V: n/V = 0.00133 g/cm^3 / M
Substitute n/V into the equation to solve for M: M = 1.4 g / [(0.00133 g/cm^3 / M) (0.08206 L.atm/K.mol) (298.15 K) (1 cm^3 / 1 x 10^-6 L)]
Simplifying this equation gives: M = 28.97 g/mol
Therefore, the molar mass of the gas is approximately 28.97 g/mol.