Combine gas law problem

Question

For many purposes we can treat ammonia (NH3) as an ideal gas at a temperature above it’s boiling point of 133 degrees celsius. Suppose the temperature of a sample of ammonia gas is lowered from 62.0 degrees celsius to 12.0 degrees celsius, and at the same time the pressure is increased by 15.0%. Does the volume of the sample increase, decrease, or stay the same? If you said the volume increases or decreases, calculate the percentage change in the volume.

Answer 1

You always want to solve change problems multiplicatively so a 10% increase is 1.1 times and a 5% decrease is .95 times.

I prefer to just use PV=nRT to remind me that P and V are inverse and P,T, and V,T and n,P and n,V are proportional. This allows me to write:

V is proportional to T and inverse with P so

V₂/V₁ = (T₂/T₁)(P₁/P₂)

When you use this analysis, all measures must be in absolute unit (They are 0 when the quantity is 0: Kelvin for temperature and absolute pressure in any units (not gauge pressure!))

We are told to find the percent change which is (V₂-V₁)/V₁ (actually the fractional change - you multiply by 100 to get percent). This is also V₂/V₁ - 1

V₂/V₁ = (285K/335K)(1/1.15) The multiplier for P is 1.15 and V is inverse to P

I'll leave the rest to you.

Answer 2

Not enough information to solve well. The boiling point given for ammonia is above the specified experimental conditions -- or is it? We don't know the initial pressure; boiling points are assumed to be standard pressure if not otherwise specified. If the ammonia is a liquid or partially liquified, the ideal gas law doesn't obviously apply!

However, the normal boiling point of NH₃ is actually -28 F. I suspect -13.3 C was the original datum? Not 133 C? But that still doesn't solve anything. What is critical here, is, what WAS the original pressure? Up to the critical point for ammonia (~405 K), there is still the possibility of condensing ammonia with sufficiently high pressure and sufficiently low temperature! You can say that the volume has decreased. If you wanted to look up the pressure vs. temperature graph for ammonia, and provide original pressure limits for a volume proprotional decrease based on gas phase only throughout, you could do that.

But why throw good answers after poor questions?

--Cheers, --Mr. d.