The unknown gas with the same average velocity as atoms of argon is hydrogen fluoride (HF).
The given parameters;
- temperature of the gas, = 200 K
- temperature of the argon = 400 K
- atomic mass of argon = 40 g/mol
The average speed of an atom at a given temperature and mass is calculated as follows;
[tex]\bar V = \sqrt{\frac{8RT}{\pi M} } \\\\\bar V_{Ar} = \bar V _{X}\\\\\sqrt{\frac{8RT_{Ar}}{\pi M_{Ar}} } = \sqrt{\frac{8RT_{X}}{\pi M_{X}} } \\\\\frac{8RT_{Ar}}{\pi M_{Ar}} = \frac{8RT_{X}}{\pi M_{X}}\\\\\frac{T_{Ar}}{M_{Ar}} = \frac{T_{X}}{M_{X}}\\\\M_ X = \frac{T_ XM_{Ar}}{T_{Ar}} \\\\M_X = \frac{200 \times 40}{400} \\\\M_ X= 20 \ g/mol[/tex]
The molar mass of hydrogen fluoride is calculated as;
HF = 1 + 19 = 20 g/mol
Thus, the unknown gas with the same average velocity as atoms of argon is hydrogen fluoride (HF).
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