### If 30cm3 of a gas at 50°c is warmed to 80°c at a fixed pressure,...

If 30cm3 of a gas at 50°c is warmed to 80°c at a fixed pressure, the fractional increase in volume is?

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isaaq
8 months ago
Solution

Looks like a ratio problem and we need to include both T and V. The ideal gas law says
PV = nRT
For a ratio we need:
P1*V1 = n1*R*T1 (R is a constant)
P2*V2 = N2*R*T2
The only variables changing are V and T so lets get them to one side, and the stuff that is not changing, on the other side of the equals sign.
V1/T1 = n1*R/P1
V2/T2 = n2*R/P2
Now, neither the number of moles of gas (n) or the pressure (P1, P2) change
n1*R/P1 = n2*R/P2
and therefore
V1/T1 = V2/T2
Now, we will want to know V2 so solve for it and then put in the numbers (remember, T is in kelvin and 50º C = 323 K, 80º C is 353 K)
V2 = T2*V1/T1 = 353*30 cm3/323 = 32.79 cm3
The fractional increase in volume is how much it increased divided by what it was. The original volume was 30 cm3 and increase in volume is 2.79 so the fractional increase is
2.79/30 = 0.093
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Gaby
6 months ago
Solution
Looks like a ratio problem and we need to
include both T and V. The ideal gas law says
PV = nRT
For a ratio we need:
P1*V1 = n1*R*T1 (R is a constant)
P2*V2 = N2*R*T2
The only variables changing are V and T so
lets get them to one side, and the stuff that
is not changing, on the other side of the
equals sign.
V1/T1 = n1*R/P1
V2/T2 = n2*R/P2
Now, neither the number of moles of gas
(n) or the pressure (P1, P2) change
n1*R/P1 = n2*R/P2
and therefore
V1/T1 = V2/T2
Now, we will want to know V2 so solve for
it and then put in the numbers (remember,
T is in kelvin and 50º C = 323 K, 80º C is 353
K)
V2 = T2*V1/T1 = 353*30 cm3/323 = 32.79
cm3
The fractional increase in volume is how
much it increased divided by what it was.
The original volume was 30 cm3 and
increase in volume is 2.79 so the fractional
increase is
2.79/30 = 0.093
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victory
8 months ago
V1=30, V2=?
T1=50°»273+50
=323k
T2=80°»273+80
=353k
using charles law:
V1/T1= V2/T2
V2=V1T2/T1
=30x353/323
=10590/323
=32.786cm^3
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