Question

At constant temperature, the product of pressure and volume of a given amount of a gas is constant. This is:
A. Gay-Lussac's law
B. Charles' law
C. Boyle's law
D. Pressure law

Answer 1

Hint: The gas law which is at constant temperature is Boyle’s Law which states that under a constant temperature when the pressure on a gas increases its volume decreases. In other terms, according to Boyle’s law the volume of a gas is inversely proportional to pressure provided the temperature and the number of molecules is constant.

Complete step by step answer:
A. Gay-Lussac’s Law states that at fixed volume and mass of a gas, the pressure of that gas is directly proportional to the temperature. This mathematically can be written as:
$
  P\alpha T \\
  \dfrac{P}{T} = const \\
 $
The scale for temperature here used is Kelvin. Hence, this is not the law that represents the given statement.

B. Charles’ Law states that, at constant pressure and for constant mass, the volume of a gas is directly proportional to the temperature. Mathematically we have,
$
  \dfrac{{{V_2}}}{{{V_1}}} = \dfrac{{{T_2}}}{{{T_1}}} \\
  \dfrac{V}{T} = const \\
 $
Hence, this is not the law that represents the given statement.

C. Boyle’s Law states the relation between volume and pressure at constant temperature and mass. It states that at a constant temperature when the pressure on a gas is increased the volume of the gas decreases. In other terms, according to Boyle’s law the volume of a gas is inversely proportional to pressure provided the temperature and the number of molecules is constant. Mathematically,
$
  p\alpha \dfrac{1}{V} \\
  p = {k_1}\dfrac{1}{V} \\
  \dfrac{{{p_1}}}{{{p_2}}} = \dfrac{{{V_2}}}{{{V_1}}} \\
  {p_1}{V_1} = {p_2}{V_2} = const.({k_1}) \\
 $

Hence, this is the law that represents the given statement (Option C).

D. Pressure Law: Gay-Lussac’s law is referred as Pressure law. Hence, this is not the law that represents the given statement.

Note: A student must note that these are the laws for ideal gases for a real gas compressibility factor “z” comes into picture.Compressibility factor is nothing but the ratio of the actual molar volume of the gas to the calculated molar volume at the same temperature and pressure.