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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Gaby

6 months ago

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

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

8 months ago

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