A 5.00 liter sample of gas measured at 27.0*C and 1.25 atm presure has a mass of 10.13 g. What is the formula weight of the gas?
To find the formula weight of the gas, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure of the gas in atmospheres (atm)
V = volume of the gas in liters (L)
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas in Kelvin (K)
First, we need to convert the temperature from 27.0°C to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.
T(°C) + 273.15 = T(K)
So, let's calculate the temperature in Kelvin:
27.0 + 273.15 = 300.15 K
Next, we substitute the given values into the ideal gas law equation:
PV = nRT
(1.25 atm) * (5.00 L) = n * (0.0821 L·atm/mol·K) * (300.15 K)
Simplifying the equation:
6.25 L·atm = n * 24.63 L·atm/mol
Now, we can solve for the number of moles (n):
n = 6.25 L·atm / 24.63 L·atm/mol
n ≈ 0.253 mol
The given sample contains 0.253 moles of the gas. Finally, to find the formula weight of the gas, we use the formula:
Formula weight = mass / moles
Formula weight = 10.13 g / 0.253 mol
Formula weight ≈ 40 g/mol
Therefore, the formula weight of the gas is approximately 40 g/mol.