Question

a gas made up of atoms escapes through a pinhole 1.87 times as fast as cl₂ gas. write the chemical formula of the gas.

Explanation:

Step1: Recall Graham's Law

$\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$ where $v$ = speed, $M$ = molar mass.

Step2: Assign values

Let $v_1$ = unknown gas speed, $v_2$ = Cl₂ speed. Given $\frac{v_1}{v_2}=1.87$, $M_2$ (Cl₂) = 70.90 g/mol.

Step3: Solve for $M_1$

$1.87 = \sqrt{\frac{70.90}{M_1}}$ → Square both sides: $1.87^2 = \frac{70.90}{M_1}$ → $M_1 = \frac{70.90}{1.87^2}$

Step4: Calculate $M_1$

$1.87^2 ≈ 3.4969$ → $M_1 ≈ \frac{70.90}{3.4969} ≈ 20.3$ g/mol. The atomic gas with molar mass ~20.3 is Ne.

Answer:

Ne