What will cause the volume of an ideal gas to triple in value?

The volume of an ideal gas will triple in value if the pressure is reduced to one-third of its initial value

Explanation:

We can determine this from the gas laws. Using Boyle's law, which states that "the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature"

Mathematically, P ∝ (1/V)

Since P ∝ (1/V), we can then write that

P = k(1/V)

Where P is the pressure, V is the volume and k is the proportionality constant

PV = k

We can then write that

P1V1 = P2V2 = P3V3 = ...

Hence, P1V1 = P2V2

Where P1 is the initial pressure of the gas

P2 is the final pressure of the gas

V1 is the initial volume of the gas

and V2 is the final volume of the gas

From the question, we want to determine what will make the new volume be thrice the initial volume.

Hence,

P1 = P

V1 = V

P2= ??

V2 = 3V

Therefore,

P × V = P2 × (3V)

P2 = PV/3V

P2 = P/3 = 1/3(P)

This means the volume of an ideal gas will triple in value if the pressure is reduced to one-third of its initial value

To triple the volume of an ideal gas in value, keeping the temperature constant, the pressure must be reduced by a factor of 3 to maintain the inverse proportionality and the value of k (which is a constant and must not vary).

Explanation:

The correct question is with options, as follow:

"Which of the following will cause the volume of an ideal gas to triple in value?

A) Raising the temperature from 25°C to 75°C at constant pressure.

B) Lowering the absolute temperature by a factor of 3 at constant pressure.

C) Raising the absolute temperature by a factor of 3 while increasing the pressure by a factor of 3.

D) Lowering the absolute temperature by a factor of 3 while increasing the pressure by a factor of 3.

E) Lowering the pressure by a factor of 3 while the temperature stays constant."

Pressure and volume are related by Boyle's law, which says:

"The volume occupied by a given gas mass at constant temperature is inversely proportional to the pressure"

Boyle's law is expressed mathematically as:

Pressure * Volume = constant

o P * V = k

In this law, two variables are then related: pressure and volume, so it is assumed that the temperature of the gas and the number of molecules in the gas are constant.

To triple the volume of an ideal gas in value, keeping the temperature constant, the pressure must be reduced by a factor of 3 to maintain the inverse proportionality and the value of k (which is a constant and must not vary). So, is option E.

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