The label of a gas cylinder has come off in your laboratory. you know that only one species of gas is contained in the cylinder, but you do not know whether it is hydrogen, oxygen, or nitrogen. to find out, you evacuate a 5-liter flask, seal it and weigh it, then let gas from the cylinder flow into it until the gauge pressure equals 1.00 atm. the flask is reweighed, and the mass of the added gas is found to be 13.0 g. room temperature is 27 °c, and barometric pressure is 1.00 atm. which gas is it? state your assumptions.

The correct option is: Oxygen

Explanation:

According to the Ideal Gas Equation: P.V = n. R.T

Here, R - ideal gas constant, P - absolute pressure, V - volume, T - temperature, n - number of moles of gas.

Also, n = given mass of gas (w) ÷ molar mass of gas (M)

Given: P = gauge pressure + barometric pressure = 1 atm + 1 atm = 2 atm; V = 5 L; w = 13 g; R = 0.08206 L·atm·mol⁻¹·K⁻¹; T = 27 °C = 27°C + 273.15 = 300.15K                          (∵ 0°C = 273.15 K).

Since, P.V = n. R.T = (w ÷ M) . R.T

⇒ M = (w. R.T) ÷  (P.V) = (13g × 0.08206 L·atm·mol⁻¹·K⁻¹ × 300.15K)÷(2atm × 5 L)

⇒ M = 32 g.mol⁻¹

As we know, the molar mass of oxygen gas (O₂) is 32 g.mol⁻¹.

Therefore, the gas is oxygen.