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A gas is in a Sealed container. The pressure is tripled and the temperature is doubled.

a. does the number of molecules within the container increase. decrease or stay the same?

b. By what factor does the number density of the gas increases.

Short Answer

Expert verified

a. The number of molecules remains constant as the container is sealed.

b. The number density of the gas in the container increases by 1.5 times.

Step by step solution

01

Step 1. Theory of  molecule 

As per Avogadro statement, in a constant temperature and volume, all gas molecules in a closed container remains the same. As container is closed, all number of molecules are constant in the container.

02

Formula of density  

The equation of initial density ND1is;

(ND1)=n1V1=P1RT1

Where n1is the initial number of molecules, V1is initial volume, P1initial pressure, and T1is initial temperature.

The equation of final density ND2is;

(ND2)=n2V2=P2RT2

Where is final number of molecule, V2is final volume, P2is the final pressure T1is the final Temperature.

(ND2)(ND1)=P2RT2ร—RT1P1=P2P1ร—T1T2

Now put the value 3 P1atP2and2T1toT2

(ND2)(ND1)=3P12T1ร—T1P1(ND2)=32(ND1)=1.5(ND1)

So, the final number of density is 1.5times.

The density of the gas in the container thus increases by 1.5 times.

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