The speed of sound in a certain monatomic gas is $320\text{ m/s}$ at room temperature ($20\mathrm{℃}$). What gas is this?

• A. Helium
• B. Neon
• C. Krypton
• D. Xenon
• E. Argon

Answer: (E)

Verified step by step guidance

1. Understand that the speed of sound in a gas is given by the formula: $v=\sqrt{\frac{\gamma RT}{M}}$, where $v$ is the speed of sound, $\gamma$ is the adiabatic index, $R$ is the universal gas constant, $T$ is the temperature in Kelvin, and $M$ is the molar mass of the gas.
2. Convert the given temperature from Celsius to Kelvin using the formula: $T$_k = T_℃ + 273.15. For 20℃, this becomes $293.15$ K.
3. Recognize that for a monatomic gas, the adiabatic index $\gamma$ is $5/3$.
4. Rearrange the speed of sound formula to solve for the molar mass $M$: $M=\frac{\gamma RT}{v^2}$.
5. Substitute the known values into the rearranged formula: $\gamma =\; 5/3$, $R=\; 8.314$ J/(mol K), $T=\; 293.15$ K, and $v=\; 320$ m/s. Calculate $M$ to identify the gas.