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A sample of gas starts at 1.00 atm, 0.00° C, and 30.0 mL. What is the volume if the temperature increases to 27.0° C and the pressure increases to 2.00 atm?

User Takrishna
by
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1 Answer

3 votes

Answer:

16.48 mL.

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial pressure (P₁) = 1 atm

Initial temperature (T₁) = 0 °C

Initial volume (V₁) = 30 mL

Final temperature (T₂) = 27 ° C

Final pressure (P₂) = 2 atm

Final volume (V₂) =?

Next, we shall convert celsius temperature to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T₁) = 0 °C

Initial temperature (T₁) = 0 °C + 273

Initial temperature (T₁) = 273 K

Final temperature (T₂) = 27 °C

Final temperature (T₂) = 27 °C + 273

Final temperature (T₂) = 300 K

Finally, we shall determine the final volume of the gas. This can be obtained as:

Initial pressure (P₁) = 1 atm

Initial temperature (T₁) = 273 K

Initial volume (V₁) = 30 mL

Final temperature (T₂) = 300 K

Final pressure (P₂) = 2 atm

Final volume (V₂) =?

P₁V₁ / T₁ = P₂V₂ / T₂

1 × 30 / 273 = 2 × V₂ / 300

30 / 273 = 2 × V₂ / 300

Cross multiply

273 × 2 × V₂ = 30 × 300

546 × V₂ = 9000

Divide both side by 546

V₂ = 9000 / 546

V₂ = 16.48 mL

Therefore, the final volume of the gas is 16.48 mL.

User Patryk Kubiak
by
8.5k points
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