Question

The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. But given the same kinetic energies, a lighter molecule will move faster than a heavier molecule. Where R=8.314 J/(mol·K) and ℳ is molar mass in kilograms per mole. Note that a joule is the same as a kg·m2/s2.

What is the rms speed of O2 molecules at 429 K?

What is the rms speed of He atoms at 429 K?

Glycine is an amino acid with the formula C2H5NO2. Determine the number of moles of carbon in 24.99 g of glycine?

Answer 1

1. rms speed of O2 molecule at 429K

rms speed = (3RT/M)^1/2

where, R = 8.314kg.m²/s²molK

T = Temperature in K = 429K

M = molar mass in kg/mol = 0.032kg/mol

keeping all the values-

rms speed = (3*8.314kgm²/s²molK*429K / 0.032kg/mol )^1/2

= (334378.6875 m²/s²)^1/2

rms speed = 578.25m/sec

2. for helium, R and T remains the same

Molar mass, M = 0.004 kg/mol

rms speed of He = (3*8.314kgm²/sec²molK*429K / 0.004kg/mol)^1/2

=(2675029.5m²/sec²)^1/2

rms speed of He atoms = 1635.6m/sec

3. Mass of glycine given = 24.99g

Molar mass of glycine = 75.06g/mol

so, moles of glycine in 24.99g = mass/molar mass = 24.99g/75.06g/mol = 0.3329moles

now,as per the formula,

1 mole of glycine has 2 moles of Carbon.

so, 0.3329 moles of glycine has = 2*0.3329moles = 0.666moles of Carbon.