To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 4.3-L bulb, then filled it with the gas at 1.90 atm and 21.0 C and weighed it again. The difference in mass was 9.5 g . Identify the gas.

Use PV = nRT and solve for n = number of mols, the n = grams/molar mass. You know grams and n, solve for molar mass.

N2

To identify the diatomic gas (X2), we can use the ideal gas law equation, which relates pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas.

The ideal gas law equation is written as:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's convert the given temperature from Celsius to Kelvin by adding 273.15:

T = 21.0 C + 273.15 = 294.15 K

Next, rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Now, let's calculate the number of moles of gas:

n = (1.90 atm * 4.3 L) / (0.0821 L·atm/(mol·K) * 294.15 K)

n ≈ 0.295 mol

Since the mass difference is given as 9.5 g, we can use the molar mass (M) formula to determine the molar mass of the gas:

M = mass / moles

M = 9.5 g / 0.295 mol ≈ 32.20 g/mol

The molar mass of the gas is approximately 32.20 g/mol. Now we can refer to the periodic table to identify the gas that has a molar mass of 32.20 g/mol.

Upon looking at the periodic table, we find that the gas with a molar mass of approximately 32.20 g/mol is oxygen (O2). Therefore, the gas X2 in this experiment is likely oxygen (O2).