Table of contents

7. Gases

Kinetic Molecular Theory

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Multiple Choice

The urms of H2 molecules at 273 K is 1.84 × 10^3 m/s. At what temperature is the urms for H2 1.6 times greater than this value?

819 K

546 K

1000 K

700 K

Verified step by step guidance

Understand that the root mean square speed (urms) of a gas is given by the formula:

\sqrt{\frac{3 R T}{M}}

, where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

Given that the urms of H2 at 273 K is 1.84 × 10^3 m/s, we need to find the temperature at which the urms is 1.6 times this value.

Set up the equation for the new urms:

\sqrt{\frac{3 R T}{M}}

= 1.6 × 1.84 × 10^3 m/s.

Square both sides of the equation to eliminate the square root, resulting in:

\frac{3 R T}{M}

= (1.6 × 1.84 × 10^3)^2.

Solve for T by isolating it on one side of the equation: T =

\frac{M (1.6 × 1.84 × 10^3)^2}{3 R}

. Substitute the known values for M and R to find the temperature.

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