To identify a diatomic gas (x2), a researcher carried out the following experiment: She weighed an empty 3.4L- bulb, then filled it with the gas at 1.20 atm and 22.0 C and weighed it again. The difference in mass was 4.7g . Identify the gas.
Express your answer as a chemical formula.
n = PV/RT amd solve for n. Then
n = grams/molar mass
Something like 28 g. Could be N2. Could be C2H4 (ethylene). N2 is a diatomic gas, ethylene is not.
To identify the gas, we need to calculate its molar mass. The molar mass can be determined using the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given temperature of 22.0°C to Kelvin:
T = 22.0°C + 273.15 = 295.15 K
Next, let's calculate the number of moles (n) of the gas using the ideal gas law. Rearranging the equation, we have:
n = PV / RT
n = (1.20 atm) * (3.4 L) / (0.0821 L·atm/(mol·K)) * (295.15 K)
n ≈ 0.1719 mol
Now, we can calculate the molar mass (M) of the gas using the given difference in mass (4.7 g). We know that the difference in mass is equal to the molar mass multiplied by the number of moles:
molar mass = difference in mass / number of moles
molar mass = 4.7 g / 0.1719 mol
molar mass ≈ 27.3 g/mol
To identify the gas, we need to compare the molar mass to the molar masses of known diatomic gases. Some common diatomic gases include hydrogen (H2), oxygen (O2), nitrogen (N2), fluorine (F2), chlorine (Cl2), bromine (Br2), and iodine (I2).
Among these options, the diatomic gas with a molar mass closest to 27.3 g/mol is chlorine (Cl2). Therefore, the gas is likely chlorine, and its chemical formula is Cl2.