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Byju's Answer

Standard XII

Chemistry

Molecular Speeds - Vrms, Vavg, Vmps

In an experim...

Question

In an experiment of analysis of oxalate salt, a solution of oxalate gives white precipitate with $C a C l_{2}$ solution. This precipitate is dissolved in dilute $H_{2} S O_{4}$ and decolourises $K M n O_{4}$ (acidified) solution as the following reactions:
$N a_{2} C_{2} O_{4} + C a C l_{2} \to C a C_{2} O_{4} ↓ w h i t e + 2 N a C l$
$C a C_{2} O_{4} + H_{2} S O_{4} \to C a S O_{4} + H_{2} C_{2} O_{4}$
$K M n O_{4} + H_{2} S O_{4} + H_{2} C_{2} O_{4} \to M n S O_{4} + K_{2} S O_{4} + H_{2} O + C O_{2}$
If one mole of $N a_{2} C_{2} O_{4}$ is taken and reacted with sufficient amount of other reactants such as to give 100% reaction yield at each step and the liberated $C O_{2}$ is kept in a container of volume V at pressure P, temperature T. Then $U_{r m s}$ of $C O_{2}$ gas in container will be :

\sqrt{\frac{3 P V}{2 M_{C O_{2}}}}

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\sqrt{\frac{3 R T}{2 M_{C O_{2}}}}

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\sqrt{\frac{3 P V}{M_{C O_{2}}}}

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\sqrt{\frac{3 R T}{M_{C O_{2}}}}

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Solution

The correct options are
A $\sqrt{\frac{3 P V}{2 M_{C O_{2}}}}$
D $\sqrt{\frac{3 R T}{M_{C O_{2}}}}$
Applying POAC on carbon,
(moles of $N a_{2} C_{2} O_{7}) \times 2 =$ (mole of $C O_{2}) \times 1$
$1 \times 2 = n_{C O_{2}}$
$U_{r m s} = \sqrt{\frac{3 P V}{2 M_{C O_{2}}}}$
or, $U_{r m s} = \sqrt{\frac{3 R T}{M_{C O_{2}}}}$

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The correct options are A √3PV2MCO2 D √3RTMCO2Applying POAC on carbon,(moles of Na2C2O7)×2= (mole of CO2)×11×2=nCO2Urms=√3PV2MCO2 or, Urms=√3RTMCO2