Agas has a pressure of 0.410 atm and volume of 32 l. at what pressure, would the volume of the gas change to 28 l

The question here follows the ideal gas law, so we can say that the ideal gas equation is applicable which is PV = nRT
where:P is pressure,V is volume,n is number of moles, R is universal gas constant, andT is temperature. 
When the right-hand side of the equation is constant, P₁V₁ = P₂V₂ this is the existing relationship,
Substituting the given will give us:(0.410 atm)(32 L) = (P₂)(28 L)P₂ = 0.4686

It shows that the experiment is designed properly.