A certain volume of a gas had a pressure of 800 torr at a temperature of -40 degrees C. What was the original volume if the volume at STP is now 450.0 cm^3?

Question

the correct answer is 365 cm^3. I just need an explanation. Thank you!

Answer 1

To get to this answer, you just use the equation...

P₁V₁/T₁ = P₂V₂/T₂

800 V/(-40 + 273.15) = 760 * 450 / 273.15

To find the original volume, you would just solve for V in the equation above. Your initial pressure was 800 torr, but in the second scenerio, it decreases to 760 (since standard pressure is 1 atm or 760 torr). However, your temperature increases from -40^oC to 0^oC (or 273.15K). A decrease in pressure would cause volume to increase (since they are inversely proportional), and an increase in temperature would also cause an increase in volume (since they are directly proportional). Therefore the increase in temperature and increase in pressure both contribute to a higher volume in the second scenario (or conversely a smaller volume in the first scenario).

Answer 2

You use the combined gas law P₁V₁/T₁=P₂V₂/T₂. At STP p=1 atm (or 760 torr) and the temperature is 0 degrees C (273K). Substitute for the various quantities and solve for V1, 364.9 cm³ .