In an experiment of analysis of oxalate salt, a solution of oxalate gives white precipitate with CaCl2 solution. This precipitate is dissolved in dilute H2SO4 and decolourises KMnO4 (acidified) solution as the following reactions.
Na2C2O4 + CaCl2 → CaC2O4 + 2NaCl
white
CaC2O4 + H2SO4 → CaSO4 + H2C2O4
2KMnO4 + 3H2SO4 + 5H2C2O4 → 2MnSO4 + K2SO4 + 8H2O + 10CO2
If one mol of Na2C2O4 is taken and reacted with sufficient amount of other reactants such as to give 100% reaction yield at each step and the liberated CO2 is kept in a container of volume 'V' at pressure 'P' , temperature 'T'. Then Urms of CO2 gas in container will be
1 mol Na2C2O4 → 1 mol CaC2O4 [from reaction (i)]
1 mol CaC2O4 → 1 mol H2C2O4 [from reaction (ii)]
1 mol H2C2O4 → 2 mol CO2 [from reaction (iii)]
⇒ = 2
Urms =
For CO2 gas
Urms =
The root mean square speed (Urms) is a measure of the average speed of gas molecules in a sample, derived from kinetic theory. It depends on the temperature (T), molar mass (M), and the gas constant (R), and is given by:
In this problem, we are to find Urms for CO2 gas produced in the reactions. Note that Urms is independent of pressure (P) and volume (V) of the container; it depends only on T and M.
Step 1: Determine moles of CO2 produced from 1 mol of Na2C2O4
From the given reactions:
Na2C2O4 produces CaC2O4, which then produces H2C2O4 (oxalic acid).
In the final reaction: 5H2C2O4 produces 10CO2.
So, 5 moles of H2C2O4 produce 10 moles of CO2, meaning 1 mole of H2C2O4 produces 2 moles of CO2.
Since 1 mole of Na2C2O4 produces 1 mole of H2C2O4, it will produce 2 moles of CO2.
Step 2: Relate Urms to given parameters
Urms for CO2 is given by:
It does not depend on P or V, nor on the amount of gas (number of moles).
Step 3: Compare with the options
Option 1: — This matches the standard formula.
Option 2: — Incorrect, as it involves P and V.
Option 3: — Incorrect, due to P and V.
Option 4: — Incorrect, due to the factor of 2 in denominator.
Final Answer: The correct expression is .
Root Mean Square Speed:
Where R is the gas constant, T is temperature in Kelvin, and M is molar mass.
Note: Urms is independent of pressure and volume; it is a function of temperature and molar mass only.
Ideal Gas Law: PV = nRT, which relates pressure, volume, moles, and temperature, but is not directly used in calculating Urms.
Identify the correct labels of A, B and C in the following graph from the options given below : Root mean square speed (Vrms) ; most probable speed (Vmp); Average speed (Vav)
