Question

To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 2.8-L bulb, then filled it with gas at 1.60 atm.

and 30.0 °C and weighed it again. The difference in mass was 5.1 g. Identify the gas.
Express your answer as a chemical formula.

Answer 1

To identify the diatomic gas (X2), the researcher filled a 2.8-L bulb with the gas at 1.60 atm and 30.0 °C. The difference in mass was 5.1 g. By calculating the molar mass of the gas and comparing it to known gases, we can determine its identity. The molar mass of 36.17 g/mol matches with chlorine (Cl2), making the chemical formula for the gas Cl2.

Step-by-step explanation:

To identify a diatomic gas (X2), the researcher filled a 2.8-L bulb with the gas at 1.60 atm and 30.0 °C. After weighing the bulb again, the difference in mass was 5.1 g. To determine the identity of the gas, we need to calculate its molar mass and compare it to known gases.

First, we use the ideal gas law to calculate the number of moles of gas:

n = PV / RT = (1.60 atm) * (2.8 L) / ((0.08206 L·atm/(mol·K)) * (30.0 + 273.15 K)) = 0.141 mol

Next, we calculate the molar mass of the gas using the mass difference and the number of moles:

Molar mass = Mass difference / Moles = 5.1 g / 0.141 mol = 36.17 g/mol

Comparing this molar mass to known gases, we find that it matches with the diatomic gas chlorine (Cl2). Therefore, the chemical formula for the gas is Cl2.