Question

A gas has a pressure of 5.7 atm at 100.0°C. What is its pressure at20.0°C (Assume volume is unchanged)

Answer 1

`\large \boxed{\text{4.5 atm}}`

Step-by-step explanation:

The volume and amount of gas are constant, so we can use Gay-Lussac’s Law:

At constant volume, the pressure exerted by a gas is directly proportional to its temperature.

`(p_(1))/(T_(1)) = (p_(2))/(T_(2))`

Data:

p₁ =5.7 atm; T₁ = 100.0 °C

p₂ = ?; T₂ = 20.0 °C

Calculations:

1. Convert the temperatures to kelvins

T₁ = (100.0 + 273.15) K = 373.15

T₂ = (20.0 + 273.15) K = 293.15

2. Calculate the new pressure

`\begin{array}{rcl}(5.7)/(373.15) & = & (p_(2))/(293.15)\\\\0.0153 & = & (p_(2))/(293.15)\\\\0.0153* 293.15 &=&p_(2)\\p_(2) & = & \textbf{4.5 atm}\end{array}\\\text{The new pressure will be $\large \boxed{\textbf{4.5 atm}}$}`