8. If 400 mL of gas has a temperature of 75°C, then what would be the new volume if the temperature increased to 95°C?

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