Prince of Crime

Chemistry Level pending

After the events that took place after Batman's battle with the Court of Owls, the city quietened down.

On one rainy day, Batman knew a dangerous forgotten force was back in Gotham city. As predicted, the Mayor of Gotham city had been given a dose of a lethal chemical.

The only way to save the Mayor was to answer the question that had been written on the wall of the Mayor's office,

What is the value of constant volume heat capacity for the compound present in laughing gas ?

11 R 2 \frac{11R}{2} 13 R 2 \frac{13R}{2} 9 R 2 \frac{9R}{2} 15 R 2 \frac{15R}{2}

Vitthal Yellambalse by Vitthal Yellambalse , 22, India

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1 solution

To calculate constant volume heat capacity we must find the number of degrees of freedom that laughing gas possesses.

Laughing gas is N 2 N_{2} O

Number of translational degrees of freedom = 3

Number of Rotational degrees of freedom = 2 {Linear molecule}

Number of Vibrational degrees of freedom:

Elements in the compound = 1 Nitrogen + 2 Oxygen = 3

Since the compound is linear, 3n-5 can be used to find vibrational degrees of freedom, 3(3)-5 = 4

So constant volume heat capacity = [0.5(3+2) + 4]R

= 13 R 2 \frac{13R}{2}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Why didn't you take 0.5 of 4 also,

The formula for Cv is fR/2. Isn't it? ( f is total number of degree of freedom)

And please tell me about the formula u used for calculating Vibrational degree of freedom. Thanks. ☺

@Vitthal Yellambalse

Aniket Sanghi - 4 years, 6 months ago

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Do note that this formula is only applicable for molecules that have more that 3 constituent atoms, for the diatomic case there are only 2 degrees of vibrational freedom.

Vitthal Yellambalse - 4 years, 6 months ago

Also, isn't the vibrational degree of freedom considered only at high temperatures??

Also, I know one case which is somewhat contradicting - we are told that for linear diatonic molecule at high temperature vibrational degree of freedom is 2 . But from your formula it is coming 1.

Aniket Sanghi - 4 years, 6 months ago

Wait , do your formula tell about half the degree of freedom (for vibrational)???

Aniket Sanghi - 4 years, 6 months ago

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