this is number from kaplan blue book page 670 number 44

Q. A rigid container holds 3.00 moles of an ideal gas at 298K. How many moles of gas would need to be added to the container at constant temperature to increase the pressure from 1.00 atm to 1.80 atm?

answer : 2.4 moles

the first solution says

pressure has slightly less than doubled.

temperature and volume are not changing so number of moles of gas needs to increase proportionally.

I thought that volume and pressure have inversely proportional relationship.

If pressure doubled, shouldn't volume be halved? and I believe the question didn't say that the volume isn't changing.

and also, the second solution says

p1/n1 = p2/n2 = RT/V = constant

n2= (n1/p1) x p2 = (3/1) x 1.8 = 5.40 moles

5.4 - 3 = 2.4

I don't understand how they come up with the formula above.

I only know p1v1=p2v2 or MW=DRT/P formulas for ideal gas problems

so I want to know what kind of formla they used.

Q. A rigid container holds 3.00 moles of an ideal gas at 298K. How many moles of gas would need to be added to the container at constant temperature to increase the pressure from 1.00 atm to 1.80 atm?

answer : 2.4 moles

the first solution says

pressure has slightly less than doubled.

temperature and volume are not changing so number of moles of gas needs to increase proportionally.

I thought that volume and pressure have inversely proportional relationship.

If pressure doubled, shouldn't volume be halved? and I believe the question didn't say that the volume isn't changing.

and also, the second solution says

p1/n1 = p2/n2 = RT/V = constant

n2= (n1/p1) x p2 = (3/1) x 1.8 = 5.40 moles

5.4 - 3 = 2.4

I don't understand how they come up with the formula above.

I only know p1v1=p2v2 or MW=DRT/P formulas for ideal gas problems

so I want to know what kind of formla they used.

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