What is the molecular weight of an unknown gas if 2.5g of it occupies 2L at 630 torr and a temp. of 600K?
10.2
36.6
74.3
28.9
40.1
PV = nRT and solve for n = number of moles. Then n = grams/molar mass
To determine the molecular weight of the unknown gas, you 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, and T is the temperature.
First, convert the given pressure from torr to atm. Since 1 atm = 760 torr, divide 630 torr by 760 to get the pressure in atm: 630 torr / 760 torr/atm = 0.82895 atm.
Next, convert the given volume from liters to m^3. Since 1 m^3 = 1000 L, divide 2 L by 1000 to get the volume in m^3: 2 L / 1000 L/m^3 = 0.002 m^3.
Next, convert the temperature from Kelvin to Celsius by subtracting 273.15. 600 K - 273.15 = 326.85 °C.
Now, convert the temperature from Celsius to Kelvin by adding 273.15. 326.85 °C + 273.15 = 600 K.
Using the ideal gas law equation, we have PV = nRT. Solving for n (number of moles), we get n = (PV) / (RT). Substitute the given values into the equation:
n = (0.82895 atm)(0.002 m^3) / [(0.0821 L⋅atm/(mol⋅K))(600 K)]
Calculating this expression, we get n ≈ 0.0013 mol.
To find the molecular weight (M), we can use the equation M = m / n, where m is the mass of the gas in grams and n is the number of moles.
Substitute the given mass into the equation:
M = 2.5 g / 0.0013 mol ≈ 192.3 g/mol.
Therefore, the molecular weight of the unknown gas is approximately 192.3 g/mol. None of the options you provided match the calculated value, so it seems there may be an error in the given options.