Question

An aluminum can holds 350 mL of gas at 0 C and 1.0 atm. what is the new volume if the can is heated to 10 C and the pressure inside the can rises to 75 atm?

Answer 1

4.84mL

Step-by-step explanation:

Step 1:

Data obtained from the question. This include the following:

Initial volume (V1) = 350mL

Initial temperature (T1) = 0°C

Initial pressure (P1) = 1atm

Final temperature (T2) = 10°C

Final pressure (P2) = 75atm

Final volume (V2) =...?

Step 2:

Conversion of celsius temperature to Kelvin temperature.

This can be achieved by using the formula below:

T(K) = T (°C) + 273

Initial temperature (T1) = 0°C

Initial temperature (T1) = 0°C + 273 = 273K

Final temperature (T2) = 10°C

Final temperature (T2) = 10°C + 273 = 283K

Step 3:

Determination of the new volume.

The new volume can be obtained by using the general gas equation as follow:

P1V1/T1 = P2V2/T2

1 x 350/273 = 75 x V2/283

Cross multiply

273 x 75 x V2 = 1 x 350 x 283

Divide both side by 273 x 75

V2 = (1 x 350 x 283) / (273 x 75)

V2 = 4.84mL

Therefore, the new volume is 4.84mL

Answer 2

Final volume of the gas is 4.837mL

Step-by-step explanation:

Initial volume (V1) = 350mL = 0.35L

Initial temperature (T1) = 0°C = (0 + 273.15)k = 273.15k

Initial pressure (P1) = 1.0atm

Final volume (V2) = ?

Final temperature (T2) = 10°C = (10 + 273.15)k = 283.15K

Final pressure (P2) = 75atm

To solve this question, we'll have to use combined gas equation which is the combination of all gas law I.e Charle's laws, Boyle's law, Pressure law etc.

According to combined gas equation,

(P1 × V1) / T1 = (P2 × V2) / T2

Make V2 the subject of formula,

V2 = (P1 × V1 × T2) / (P2 × T1)

V2 = (1.0 × 0.35 × 283.15) / (75 × 273.15)

V2 = 99.1025 / 20,486.25

V2 = 0.004837L

V2 = 4.837mL

The final volume of the gas is 4.837mL