Boyle's law can be expressed mathematically as

Analysis

The question asks for the mathematical representation of Boyle's Law, which describes the relationship between the pressure and volume of a fixed mass of gas at a constant temperature.

Concept Explanation

Boyle’s Law states that for a given mass of an ideal gas at a constant temperature, the volume ($V$) of the gas is inversely proportional to its pressure ($P$).

Mathematically, this is expressed as: $V \propto \frac{1}{P}$

To remove the proportionality sign and turn it into an equation, we introduce a constant ($K$): $V = K \times \frac{1}{P}$

By multiplying both sides by $P$, we get: $PV = K$

Where:

• P = Pressure
• V = Volume
• K = A constant (for a given mass of gas at a constant temperature)

Step-by-Step Solution

1. Identify the variables: Boyle's Law relates Pressure ($P$) and Volume ($V$).
2. Apply the proportionality: Since $V$ is inversely proportional to $P$, as one increases, the other decreases.
3. Form the equation: $V = \frac{K}{P}$.
4. Rearrange: Multiplying both sides by $P$ gives $PV = K$.
5. Compare with options: • A. $PV = K$ (Matches our derivation) • B. $PV = RT$ (This is the Ideal Gas Law, $PV = nRT$) • C. $V = KT$ (This relates to Charles's Law, where $V \propto T$) • D. $\frac{V}{T} = K$ (This is the mathematical form of Charles's Law)

Exam Tip

To remember the gas laws easily, use the mnemonic "TV is Great":

• T (Temperature) is constant for Boyle's Law ($PV = K$).
• P (Pressure) is constant for Charles's Law ($\frac{V}{T} = K$).
• V (Volume) is constant for Pressure Law ($\frac{P}{T} = K$).