Answer:
According to the ideal gas law, if you reduce the volume of a container to half of its original size while keeping the temperature and amount of gas constant, the pressure of the gas will double.
The ideal gas law is expressed as:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
When you decrease the volume (V) while keeping the other variables constant, the equation can be rearranged as:
P₁V₁ = P₂V₂
Where the subscripts 1 and 2 represent the initial and final conditions, respectively.
If the volume is reduced to half (V₂ = 0.5V₁), the equation becomes:
P₁V₁ = P₂(0.5V₁)
Simplifying the equation:
P₁ = 2P₂
This means that the initial pressure (P₁) is twice the final pressure (P₂) when the volume is reduced to half. In other words, decreasing the volume of the container by a factor of two results in doubling the pressure of the gas inside the container, assuming the temperature and the amount of gas remain constant.