Scientists calculate the pressure within a gas by using the following equation: $$ P=\frac{N \times k \times T}{V} $$ In the equation: \(P\) is the pressure of the gas; \(N\) is the number of particles in the gas; \(k\) is a constant; \(T\) is the temperature of the gas; \(V\) is the volume of the gas. If the number of particles in the gas decreases, which of the following changes will result in an increase in the pressure of the gas? A. decreasing both the volume and the temperature of the gas B. increasing both the volume and the temperature of the gas C. increasing the volume and decreasing the temperature of the gas D. decreasing the volume and increasing the temperature of the gas

Step by step solution

01

Option A

Decreasing both the volume and the temperature of the gas. Since the number of particles decreases, in order to maintain the same pressure, the ratio of the temperature and volume should remain constant. However, in this option, we decrease both the temperature and volume. This would cause the pressure to decrease as well as the ratio \(\frac{T}{V}\) would decrease overall, which is not what we are looking for.

02

Option B

Increasing both the volume and the temperature of the gas. In this case, we increase both the temperature and volume, so the ratio of temperature and volume is likely to change. Since both sides are increasing, the ratio \(\frac{T}{V}\) must increase to compensate for the decrease in the number of particles. Since the pressure formula is directly proportional to the temperature and inversely proportional to the volume, this option could potentially result in an increase in the pressure.

03

Option C

Increasing the volume and decreasing the temperature of the gas. In this case, the temperature decreases and the volume increases. The pressure of the gas will decrease as the ratio \(\frac{T}{V}\) decreases. This option will not result in an increase in the pressure of the gas.

04

Option D

Decreasing the volume and increasing the temperature of the gas. In this option, the volume decreases and the temperature increases. This affects the ratio \(\frac{T}{V}\) as it increases. Since the pressure of the gas is directly proportional to the temperature and inversely proportional to the volume, this option will result in an increase in the pressure of the gas. Considering the above analysis, the answer is

05

Option D

decreasing the volume and increasing the temperature of the gas would increase the pressure of the gas while also considering the decrease in the number of particles.

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