In a given diffusion apparatus, 15.0 mL of HBr gas diffuses in 1.0 min . In the same apparatus a

step 1 For this question, the root mean square velocity is inversely proportional to the square root of

In a given diffusion apparatus, 15.0 mL of HBr gas diffuses...

In a given diffusion apparatus, 15.0 $\mathrm{mL}$ of HBr gas diffuses in 1.0 $\mathrm{min}$ . In the same apparatus and under the same conditions, 20.3 $\mathrm{mL}$ of an unknown gas diffuses in 1.0 $\mathrm{min}$ . The unknown gas is a hydrocarbon. Find its molecular formula.

Key Concepts

Rate of Gas Diffusion

The rate of diffusion refers to how quickly a gas spreads or escapes through an opening or medium. When comparing different gases under the same conditions, differences in the observed diffusion rates can be attributed to variations in their molecular weights according to the inverse square root relationship highlighted in Graham's Law.

Molar Mass Determination

Determining the molar mass of an unknown gas involves comparing its diffusion rate to that of a gas with a known molar mass. Using the proportionality from Graham's Law, one can calculate the molar mass of the unknown gas by relating the ratio of their diffusion rates to the square root of the inverse ratio of their molar masses.

Graham's Law of Diffusion

Graham's Law states that the rate of gas diffusion is inversely proportional to the square root of its molar mass under constant temperature and pressure. This principle allows us to compare the diffusion rates of two different gases to deduce information about their relative molar masses.

Empirical Formula Determination for Hydrocarbons

For hydrocarbons, once the molar mass is determined, the molecular formula can be inferred by expressing the compound in the general form C?H?. By comparing the computed molar mass with the sum of the atomic masses of carbon and hydrogen atoms, the values of x and y can be deduced, leading to the determination of the molecular formula.

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