Agas at stp has a volume of 1.0 liter. if the pressure is doubled and the temperature remains constant, the new volume of the gas will

PV = nRT

A gas at STP... This means that the temperature is 0°C and pressure is 1 atm.
R is the gas constant which is 0.08206 L*atm/(K*mol)

Rearranging for volume
V = nRT/P

The temperature and number of moles are held constant. This means that this uses Boyle's Law. (The ideal gas law could be manipulated to give us this result when T and n are held constant.)
PV = k
where k is a constant.

This means that
P₁V₁ = k = P₂V₂
P₁V₁ = P₂V₂

(1 atm) * (1 L) = (2 atm) * V₂
V₂ = 0.5 L

The new volume of the gas is 0.5 L.