Question

Two vessels are labeled A and B. Vessel A contains NH3 gas at 87°C, and vessel B contains Ne gas at the same temperature. If the average kinetic energy of NH3 is 7.1 × 10−21 J/molecule at 70°C, calculate the root-mean-square speed of Ne atoms in m/s.

Answer 1

The average kinetic energy of a molecule is given by the formula: KE = (3/2)kT

where k is the Boltzmann constant, T is the temperature in kelvin.

To calculate the root-mean-square speed (v_rms) of Ne atoms, we can use the formula: v_rms = √((3kT)/m, where m is the mass of a Ne atom.

First, we need to convert the temperature of NH3 gas to kelvin: T_A = 87°C + 273.15 = 360.15 K

The average kinetic energy of NH3 at this temperature is given as 7.1 × 10−21 J/molecule.

We can rearrange the first formula to solve for k: k = 2/3 * (KE/T)

Substituting the values for KE and T_A, we get:

k_A = 2/3 * (7.1 × 10−21 J/molecule) / 360.15 K

= 3.3 × 10−26 J/K

The mass of a Ne atom is approximately 20 atomic mass units (u) or 3.32 × 10−26 kg.

Substituting the values of k and m into the second formula, we get:

v_rms = √((3kT)/m)

= √((3 * 3.3 × 10−26 J/K * 360.15 K) / (3.32 × 10−26 kg))

= 437.3 m/s (rounded to three significant figures)

Therefore, the root-mean-square speed of Ne atoms in vessel B is approximately 437 m/s at 87°C

Step-by-step explanation:

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