Question

12) We have a jar A filled with gas characterised by parameters P, V and T and another jar B filled with a gas with parameters 2P, V/4 and 2T, where the symbols have the usual meanings. The ratio of the number of molecules in jar A to those in jar B is
a) 1:1
b) 1:2
c) 2:1
d) 4:1​

Answer 1

correct option is D) 4:1

explanation =

pv=nrt

for jar a

nA=p(a)v(a)/rt(a)

for jar b

nb=p(b)v(b)/rt(b)

dividing both

we get

na/nb=4t/t

=4/1

so answer is 4:1

~vinay :-)

Answer 2

The ratio of the number of molecules in jar A to those in jar B is, (d) 4 : 1

Explanation :

Using ideal gas equation:

$PV=nRT$

Or,

$n=\frac{PV}{RT}$

The expression of the number of molecules in jar A is:

$n_A=\frac{PV}{RT}$          ..........(1)

The expression of the number of molecules in jar B is:

$n_B=\frac{(2P)\times (\farc{V}{4})}{R\times (2T)}$

$n_B=\frac{PV}{4RT}$          ............(2)

Now dividing equation 1 by 2, we get:

$\frac{n_A}{n_B}=\frac{(\frac{PV}{RT})}{(\frac{PV}{4RT})}$

$\frac{n_A}{n_B}=\frac{4}{1}$

Thus, the ratio of the number of molecules in jar A to those in jar B is, 4 : 1

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