Final answer:
To identify a diatomic gas X2, we use the Ideal Gas Law to calculate the number of moles from the given pressure and temperature, then calculate the molar mass using the gas's mass. By comparing the calculated molar mass to known diatomic gases, we can identify the gas.
Step-by-step explanation:
To identify the diatomic gas (X2), we can use the Ideal Gas Law PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Here's how we use the data provided to find the gas's identity:
- We need to convert the temperature to Kelvin: T(K) = 23.0 + 273.15 = 296.15 K
- With the pressure (P) at 1.10 atm and the volume (V) at 1.00 L, we can calculate the number of moles of gas (n).
- We then calculate the molar mass (MM) by dividing the mass of gas (1.27 g) by the number of moles (n).
- Finally, we compare the calculated molar mass with the molar masses of known diatomic gases to identify the unknown gas.
Using the Ideal Gas Law, we rearrange the formula to solve for n: n = PV / RT.
Algebraically solve for n (moles) using the values: n = (1.10 atm) * (1.00 L) / (0.0821 L*atm/mol*K * 296.15 K).
After calculating n, we find the molar mass (MM) using the difference in mass: MM = 1.27 g / n moles.
Comparing the calculated molar mass to those of known diatomic gases such as H2, N2, O2, F2, Cl2, Br2, or I2, we can identify the diatomic gas as one of these, based on the closest match.