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Question

The density of a gas at 80cm Hg and 50oC is 1.85gmL−1. What would be its density at NTP?

A
3.07g/ml
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B
2.07g/ml
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C
1.56g/ml
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D
4.5g/ml
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Solution

The correct option is C 1.56g/ml
From ideal gas equation-
PV=nRT
whereas,
P= pressure of the gas
V= volume it occupies
n= number of moles of gas present in the sample =mass of gas (m)molar mass of gas (M)
R= universal gas constant =0.0821atmLmol1K1
T= absolute temperature of the gas
PV=mMRT
PM=mVRT
As we know that,
mV=ρ(density)
PM=ρRT
For same gas,
Density of a gas is directly proportional to the pressure, i.e.,
ρPT
ρρ=PP×TT
ρ=ρ×P×TP×T
Given that:-
P=80cmHg=8076atm=1.0526
ρ=1.85gL1
T=50=(50+273)K=323K
At NTP,
P=1atm
T=20=(20+273)K=293K
ρ=?
ρ=1.85×1×2731.0526×293=1.637gL11.56gL1
Hence, density at NTP will be 1.56gL1 .

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