Chemistry related question

Question

A sample of nitrogen at pressure P is contained in a sealed syringe with a movable piston. If the volume of the sample were doubled and the absolute temperature tripled, the new pressure of the gas would be

(A) 6.0 P

(B) 5.0 P

(C)3.5 P

(D) 1.5 P

Answer 1

1. We can use the combined gas law to solve this problem:
2. (P1 V1)/T1 = (P2 V2)/T2
3. where P1, V1, and T1 are the initial pressure, volume, and absolute temperature of the nitrogen sample, respectively, and P2 and V2 are the new pressure and volume after the changes described in the problem.
4. Since the volume of the sample is doubled and the absolute temperature is tripled, we can write:
5. V2 = 2V1 (volume is doubled) T2 = 3T1 (absolute temperature is tripled)
6. Substituting these expressions into the combined gas law and solving for P2, we get:
7. P2 = (P1 V1 T2)/(V2 T1) P2 = (P1 V1 (3T1))/(2V1 T1) P2 = (3/2)P1
8. Therefore, the new pressure of the nitrogen sample would be (3/2) times the initial pressure. In other words, the answer is option (D) 1.5 P