For an ideal gas, the density of the gas is ₀ when temperature and pressure of the gas are T₀ and P₀ respectively. when the temperature of the gas is 2 ~T ₀ , its pressure becomes 3 P ₀ . The new density will be

Step-by-step solution

Applying the ideal gas law, PV = nRT , where the number of moles is expressed in terms of mass and molar mass: n = m / M , substitution gives PV = (m / M) RT . Rearranging, the density = m / V leads to P = (RT / M) , so = PM / (RT) . For the initial state with T₀ , P₀ , and ₀ , we have ₀ = P₀ M / (R T₀) . Under new conditions T = 2 T₀ and P = 3 P₀ , the new density is = (3 P₀) M / (R 2 T₀) = (3/2) (P₀ M / (R T₀)) = (3/2) ₀ . The correct option is D : 3 2 ₀ .