Welcome to the article At what temperature is the rms speed of text H 2 equal to the rms speed that text O 2 has at 313 K. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final Answer:
The temperature at which the root-mean-square (rms) speed of H2 is equal to the rms speed of O2 at 313 K is approximately 276 K.
Explanation:
The root-mean-square (rms) speed of gas molecules is related to temperature through the ideal gas law and the kinetic theory of gases. The formula for rms speed [tex](\(v_{\text{rms}}\))[/tex] is given by:
[tex]\[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \][/tex]
Where:
- [tex]\(k\)[/tex] is the Boltzmann constant [tex](\(1.38 \times 10^{-23} \, \text{J/K}\))[/tex],
- [tex]\(T\)[/tex] is the temperature in Kelvin (K), and
- [tex]\(m\)[/tex] is the molar mass of the gas.
Given that we want the rms speed of H2 [tex](\(m = 2 \, \text{g/mol}\))[/tex] to be equal to the rms speed of O2 [tex](\(m = 32 \, \text{g/mol}\))[/tex] at 313 K [tex](\(T = 313 \, \text{K}\))[/tex], we can set up the equation:
[tex]\[ \sqrt{\frac{3kT}{2}} = \sqrt{\frac{3k \times 313}{32}} \][/tex]
Solving for [tex]\(T\)[/tex]:
[tex]\[ T = \frac{313 \times 32}{2} = 4980.5 \, \text{K} \][/tex]
However, the question asks for the temperature in Celsius. Converting Kelvin to Celsius: [tex]\(276 \, \text{K}\)[/tex] is approximately [tex]\(2.85 \, \text{°C}\).[/tex]
In summary, the temperature at which the rms speed of H2 is equal to the rms speed of O2 at 313 K [tex](or \(2.85 \, \text{°C}\)).[/tex]
Learn more about Root mean square
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