Question

An ideal gas is allowed to expand from 4.00 L to 38.0 L at constant temperature. By what factor does the volume increase? factor: The pressure will increase by that same factor. decrease by that same factor. If the initial pressure was 133 atm, what is the final pressure? Pinal= atm

Answer 1

PV = nRT

At constant temperature, nRT are constant

$\Rightarrow$ PV = Constant

V₁ = 4.00L

V₂ = 38.0L

$\Rightarrow$ The volume increased by a factor of (38.0/4.00)

$\Rightarrow$ The volume increased by a factor of 9.50

Since PV has to remain a constant, if volume increases by some factor, pressure has to decreases by the same factor so as to keep product of PV a constant.

Since volume increased by a factor of 9.50, pressure decreases by the factor of 9.50

$\Rightarrow$ P₂ = P₁ / 9.50

$\Rightarrow$ P₂ = 133 atm / 9.50

$\Rightarrow$ P₂ = 14.0 atm = P_Final