Question

1. a 1.0 l flask contains 10.0 g of o₂ at 25°c.

a) what is rms speed of o₂?
b) what is the average kinetic energy of o₂?

Explanation:

Step1: Convert temperature to Kelvin

$$T = 25 + 273.15 = 298.15\ K$$

Step2: Calculate molar mass of \(O_2\)

Molar mass of \(O_2\), \(M=32\ g/mol = 0.032\ kg/mol\)

Step3: Calculate rms speed (\(v_{rms}\)) using formula \(v_{rms}=\sqrt{\frac{3RT}{M}}\)

where \(R = 8.314\ J/(mol\cdot K)\)
$$v_{rms}=\sqrt{\frac{3\times8.314\times298.15}{0.032}}$$
$$v_{rms}=\sqrt{\frac{7435.7}{0.032}}$$
$$v_{rms}=\sqrt{232365.625}\approx 482\ m/s$$

Step4: Calculate average kinetic energy (\(E_{k}\)) using formula \(E_{k}=\frac{3}{2}kT\)

where \(k = 1.38\times 10^{-23}\ J/K\)
$$E_{k}=\frac{3}{2}\times1.38\times 10^{-23}\times298.15$$
$$E_{k}=1.5\times1.38\times 10^{-23}\times298.15$$
$$E_{k}=6.17\times 10^{-21}\ J$$

Answer:

a) The rms speed of \(O_2\) is approximately \(482\ m/s\).
b) The average kinetic energy of \(O_2\) is \(6.17\times 10^{-21}\ J\).