To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 3.4-L bulb, then filled it with the gas at 1.40atm and 25.0 ∘C and weighed it again. The difference in mass was 5.5g . Identify the gas.

Use PV = nRT. You know T, R, V and P. Solve for n = number of mols, then n = grams/molar mass. Plug in g and solve for molar mass. Divide that by 2 (because it's X2) and identify from the periodic table.

N2

To identify the diatomic gas (X2), we will need to use the ideal gas law and the molar mass of the gas to determine the identity of the gas.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

We can rearrange the ideal gas law to solve for the number of moles:

n = PV / RT

First, let's convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15
T(K) = 25.0 °C + 273.15
T(K) = 298.15 K

Now we can substitute the given values into the equation:

n = (1.40 atm) x (3.4 L) / [(0.0821 L·atm/(mol·K)) x (298.15 K)]

Simplifying and calculating:

n = 0.164 mol

The difference in mass between the empty bulb and the bulb filled with the gas is 5.5 g. Since we know the number of moles (0.164 mol), we can calculate the molar mass (M) of the gas:

Molar mass (M) = Mass / Moles
M = 5.5 g / 0.164 mol

M ≈ 33.54 g/mol

Based on the calculated molar mass, we can identify the diatomic gas. The molar mass of 33.54 g/mol corresponds to nitrogen gas (N2). Therefore, the gas X2 is nitrogen gas (N2).