We are given:
V₁ = 400 mL T₁ = 75°c = (273+75)K = 348K
V₂ = x mL T₂ = 95°c = (273+95)K = 368K
Deriving Boyle's Law:
here, we can see that the volume and temperature are the only variables
from the ideal gas equation:
PV = nRT
T /V = P / nR
because P, n and R are constants, P/nR is a constant value
T / V = constant
which means that the initial and final ratio of P and T will be constant, hence:
T₁ / V₁ = T₂ / V₂, this is also known as the Charles' law. what I did above was it's derivation
Finding final volume:
plugging the given values:
348/400 = 368 / x
x = 368*400 / 348
x = 422.9 mL