According to the ideal gas law, how do temperature and pressure affect the volume of a gas, assuming the amount of gas is constant?

• A. Both increasing temperature and increasing pressure increase volume.
• B. Increasing temperature increases volume, while increasing pressure decreases volume.
• C. Both increasing temperature and increasing pressure decrease volume.
• D. Increasing temperature decreases volume, while increasing pressure increases volume.

Answer: (B)

Verified step by step guidance

1. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas (in moles), \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
2. Since the amount of gas \(n\) and the gas constant \(R\) are constant, the relationship simplifies to \(P \times V = \text{constant} \times T\).
3. To understand how volume changes with temperature and pressure, rearrange the equation to solve for volume: \(V = \frac{n \times R \times T}{P}\).
4. From this equation, observe that volume \(V\) is directly proportional to temperature \(T\) (if pressure is constant), meaning that increasing temperature increases volume.
5. Also, volume \(V\) is inversely proportional to pressure \(P\) (if temperature is constant), meaning that increasing pressure decreases volume.