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Chapter 12: Problem 58

An unknown gas effuses at one half the speed of oxygen. What is the molar mass of the unknown? It is either HBr or HI. Which gas is it?

Short Answer

Expert verified
The unknown gas is HBr.

Step by step solution

01

Understand Graham's Law

Graham's law states, rate of effusion of gas1 / rate of effusion of gas2 = \( \sqrt{ M2 / M1 } \) ,where M1 and M2 are the molar masses of the gasses. Since the rate of effusion of the unknown gas is half of that of oxygen, the ratio becomes 1 / 2 = \( \sqrt{ M_oxygen / M_unknown } \) .
02

Solve for M_unknown

Starting from the equation: 1 / 2 = \( \sqrt{ 32 g/mol / M_unknown } \) . Square both sides of the equation to find the molar mass of the unknown gas: (1 / 2)^2 = \( 32 g/mol / M_unknown \) which simplifies to: M_unknown = 4 * 32 g/mol = 128 g/mol .
03

Identify The Gas

The calculated molar mass (128 g/mol) is the same as the molar mass of iodine monobromide (HBr), which has a molar mass of around 128 g/mol. Therefore, the unknown gas is HBr.

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