A 1.44-g sample of an unknown pure gas occupies a volume of 0.336 L at a pressure of 1.00 atm and a temperature of 100.0 degrees Celsius. What is the unknown gas?
To determine the unknown gas, we can use the Ideal Gas Law equation, which relates pressure, volume, temperature, and the number of moles of gas. The equation is as follows:
PV = nRT
Where:
P = Pressure (in atmospheres)
V = Volume (in liters)
n = Number of moles
R = Universal gas constant (0.0821 L·atm/K·mol)
T = Temperature (in Kelvin)
Given:
Pressure (P) = 1.00 atm
Volume (V) = 0.336 L
Temperature (T) = 100.0 degrees Celsius
First, convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100.0 + 273.15
T(K) = 373.15 K
Now we have all the values needed to solve for the number of moles (n) of the unknown gas:
PV = nRT
n = (PV) / (RT)
n = (1.00 atm * 0.336 L) / (0.0821 L·atm/K·mol * 373.15 K)
n ≈ 0.0119 mol
Since the given sample has a mass of 1.44 g and we now know the number of moles of the unknown gas, we can calculate the molar mass (grams/mole) using the equation:
Molar mass = Mass of the sample / Number of moles
Molar mass = 1.44 g / 0.0119 mol
Molar mass ≈ 120.9 g/mol
To determine the unknown gas, we need to look up this molar mass in the periodic table. Based on the molar mass of approximately 120.9 g/mol, the unknown gas is likely Xe (Xenon).
To determine the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100.0 + 273.15
T(K) = 373.15 K
Next, we need to convert the given mass of the gas (1.44 g) to moles using the molar mass of the unknown gas. To find the molar mass, we will need the chemical formula of the gas.
Once we have the number of moles (n), we can rearrange the ideal gas law equation to solve for the molar mass (M):
P = (nRT) / V
Rewriting the equation to solve for M:
M = (mRT) / (PV)
Now we can substitute the given values into the equation:
M = (1.44 g) / [(0.0821 L·atm/mol·K) * (373.15 K) / (1.00 atm * 0.336 L)]
After calculating the value of M, we can refer to a periodic table or other reference materials to find a gas with a molar mass closest to the calculated value. This will help us identify the unknown gas.