At a pressure of 103kPa and a temperature of 22 degrees C, 52.9 g of a certain gas has a volume of 31.5 L. what is the identity of this gas?
To determine the identity of the gas, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, we need to convert the given pressure of 103 kPa into units of Pa by multiplying it by 1000:
103 kPa * 1000 = 103,000 Pa
Next, we need to convert the given temperature of 22 degrees Celsius into Kelvin. To do this, we add 273 to the Celsius temperature:
22°C + 273 = 295K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the given values, we have:
n = (103,000 Pa * 31.5 L) / (8.314 J/mol·K * 295K)
Simplifying the equation:
n = (103,000 * 31.5) / (8.314 * 295)
Calculating the value of 'n':
n ≈ 132.13 mol
Now that we have the number of moles of the gas, we can calculate the molar mass (M) of the gas using the formula:
M = mass / n
Plugging in the given mass of 52.9 g and the calculated 'n' value:
M = 52.9 g / 132.13 mol
Calculating the molar mass:
M ≈ 0.401 g/mol
Therefore, the identity of the gas can be determined by looking up its molar mass. Since the calculated molar mass is approximately 0.401 g/mol, you can find the identity of this gas in a periodic table or a database of chemical compounds.