The most probable speed of 8 g of H2 200 ms–
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1 average kinetic energy (neglect rotational and vibrational energy) of H2 gas is:
a)480 J
b)240 J
c)120 J
d)None of these.
Correct answer is option 'B'. Can you explain this answer?

Question

The most probable speed of 8 g of H2 200 ms–

1 average kinetic energy (neglect rotational and vibrational energy) of H2 gas is:
a)480 J
b)240 J
c)120 J
d)None of these.
Correct answer is option 'B'. Can you explain this answer?

Accepted Answer

Ans.

Option :

Answer

To find the most probable speed of a gas molecule, we can use the root mean square (rms) speed formula:

v_rms = √(3RT/M)

where:
v_rms = root mean square speed
R = ideal gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
M = molar mass of the gas in kg/mol

First, we need to convert the mass of H2 to molar mass:

Molar mass of H2 = 2 g/mol

Now we can calculate the number of moles (n) of H2:

n = mass / molar mass
n = 8 g / 2 g/mol
n = 4 mol

Since we have the number of moles, we can calculate the molar mass:

M = mass / n
M = 8 g / 4 mol
M = 2 g/mol

Now we need to convert the speed of 200 m/s to meters per second:

v = 200 m/s

Finally, we can calculate the most probable speed using the rms speed formula:

v_rms = √(3RT/M)
v_rms = √(3 * 8.314 J/(mol·K) * 298 K / (2 g/mol))
v_rms = √(3 * 8.314 J/(mol·K) * 298 K / (0.002 kg/mol))
v_rms = √(3 * 8.314 * 298 / 0.002) m/s
v_rms ≈ 1,927 m/s

Therefore, the most probable speed of 8 g of H2 at 200 m/s is approximately 1,927 m/s.

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