# a 300ml sample of gas at 10degree Celsius is warmed to 60 degree Celsius at a constant pressure. calculate the final volume.remember that the SI unit for volume is L. do u convert to L or u...

a 300ml sample of gas at 10degree Celsius is warmed to 60 degree Celsius at a constant pressure. calculate the final volume.

remember that the SI unit for volume is L. do u convert to L or u solve straight?

how do u determine if its a final temperature or initial temperature. sometimes its not given in the question.

thanks a bunch!

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### 2 Answers

This is an application of Charles's Law which relates changes in volume to changes in temperature. Conceptually what it says is that when you increase the temperature of a gas, the volume will also increase and when you decrease the gas temperature the volume will also decrease.

The formula is: V1/T1 = V2/T2

where V1 is the initial volume in liters or mL

T1 is the initial temperature in degrees Kelvin (K)

V2 is the final temperature in liters or mL.

T2 is the final temperature in degrees Kelvin.

To convert degrees celsius to degrees Kelvin use the formula:

K = 273.15 + degrees C

This must be done because sometimes you are dividing by the value of the temperature and if you used degrees celsius you could end up trying to divide by zero!

In your problem, to solve, first identify the variables:

V1 = 300 mL

T1 = 10 degrees celsius or 283.15 K

V2 = ?

T2 = 60 degrees celsius or 333.15 K

Substituting into the equation you get:

300/283.15 = V2/333.15

Multiply both sides by 333.15 to solve for V2 and you get:

(300 x 333.15)/283.15 = V2

V2 = 352.98 mL

To analyze similar problems look for key terms:

from usually implies an initial value

to usually implies a final value

heating usually means going from an initial T to a final T

cooling usually means going from a final T to an initial T.

As per Charles Law when pressure of a given mass of gas remains same, and the pressure and temperature change then:

V1/T1 = V2/T2

Alternately:

V2 = V1(T2/T1)

Where:

V1 = Initial Volume = 300 ml

V2 = Final volume = To be determined

T1 = Initial temperature on absolute scale = 10 + 273.15 = 283.15 Kelvin

T2 = Final temperature on absolute scale = 60 + 273.15 = 333.15 Kelvin

Substituting the given values of V1, T1 and T2 in above equation for T2:

V2 = 300*333.15/283.15 = 352.98 ml

Answer:

Final volume = 352.98 ml

Please not that any question of this type can be used solving the Universal Gas Law. As per this law for a given mass of a gas:

(Pressure x Volume)/Temperature = constant

Thus:

P1V1/T1 = P2V2/T2