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The speed of sound in a certain monatomic gas is at room temperature (). What gas is this?
A
Helium
B
Neon
C
Krypton
D
Xenon
E
Argon
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1
Understand that the speed of sound in a gas is given by the formula: , where is the speed of sound, is the adiabatic index, is the universal gas constant, is the temperature in Kelvin, and is the molar mass of the gas.
Convert the given temperature from Celsius to Kelvin using the formula: . For 20℃, this becomes K.
Recognize that for a monatomic gas, the adiabatic index is .
Rearrange the speed of sound formula to solve for the molar mass : .
Substitute the known values into the rearranged formula: , J/(mol K), K, and m/s. Calculate to identify the gas.