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Chapter 3: Q35E (page 612)

At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 20.0oC? (Hint:Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element. The molar mass of H2 is twice the molar mass of hydrogen atoms, and similarly for N2.)

Short Answer

Expert verified

At 3798C°temperature, the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules.

Step by step solution

01

Data, Assumption and Equation

Given data;

Temperature of hydrogen molecules isTH2=293k

Molar mass of hydrogen moleculesMH2=2.016g/mol

Molar mass of nitrogen moleculesMN2=28.014/mol

Assumption;

The rms speed of nitrogen molecules is equal to the rms speed of hydrogen molecules.

Equation;

Rms speed equation

Vrms=3RTM

In above equation,is constant so,T∝M

The relation between two gases is

TN2TH2=MN2MH2 ........... (1)

02

Find the temperature

From equation (1)

TN2=TH×MNMH2=293K×28.014g/mol2.016g/mol=4071k=3798C°

Hence, at 3798C°temperature, the root-mean-square speeds of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules.

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