To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 2.7-L bulb, then filled it with the gas at 1.30atm and 30.0 ∘C and weighed it again. The difference in mass was 3.9g . Identify the gas.
PV = nRT and solve for n = number of mols.
Then n = grams/molar mass. You know n and grams, solve for molar mass. Identify the gas from that. Remember some gases are diatomic.
if it was 1.1 then its Nitrogen fam my bad.
To identify the gas, we need to follow a step-by-step approach and consider the given information.
Step 1: Convert temperature from Celsius to Kelvin
To work with temperature in the ideal gas law equation, we need to convert it from Celsius to Kelvin. The formula to convert Celsius to Kelvin is:
T(K) = T(°C) + 273.15
Given T(°C) = 30.0
T(K) = 30.0 + 273.15 = 303.15 K
Step 2: Convert volume to liters
The given volume is already in liters, so no conversion is necessary.
Step 3: Convert pressure from atm to kPa
To work with pressure in the ideal gas law equation, it's better to use SI units, such as kilopascals (kPa).
1 atm = 101.325 kPa
Given P(atm) = 1.30
P(kPa) = 1.30 * 101.325 = 132.0235 kPa
Step 4: Apply the ideal gas law equation
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
To find the number of moles (n), we rearrange the equation as:
n = PV / RT
Substituting the given values into the equation:
n = (132.0235 kPa * 2.7 L) / (8.314 J/(mol·K) * 303.15 K)
Step 5: Calculate the number of moles
Now, calculate the value of n using a calculator:
n ≈ 0.345 mole
Step 6: Identify the gas using its molar mass
To identify the gas, we need to calculate its molar mass. We can do this using the difference in mass of the bulb before and after filling it with the gas.
Given the difference in mass = 3.9 g
The molar mass (M) can be calculated using the equation:
M = (difference in mass) / (number of moles)
Substituting the values:
M = 3.9 g / 0.345 mol
Step 7: Calculate the molar mass
Now, calculate the value of M using a calculator:
M ≈ 11.30 g/mol
Step 8: Identify the gas
To identify the gas, we need to find an element or compound with a molar mass close to 11.30 g/mol. Looking at the periodic table, we find that chlorine gas (Cl2) has a molar mass of approximately 70.9 g/mol.
Therefore, based on the molar mass, the gas is most likely chlorine gas (Cl2).