Question

4. Hot exhaust gases are often used in a chemical plant to heat chemical reactions before the
gases are discharged to the atmosphere. If 10.0 L of gas at 300°C and 3.00 atm expand to
125 L at 1.00 atm during the heat exchange process, what is the temperature of the gas
that is released to the atmosphere?

Answer 1

Answer:

1,250 °C

Explanation:

To find the new temperature, you need to use a variation of the Combined Gas Law. The equation looks like this:

P₁V₁ / T₁ = P₂V₂ / T₂

In this formula, "P₁", "V₁" and "T₁" represent the initial pressure, volume, and temperature. "P₂", "V₂", and "T₂" represent the final pressure, volume, and temperature. You can find the new temperature by plugging the given values into the equation and simplifying.

P₁ = 3.00 atm                      P₂ = 1.00 atm

V₁ = 10.0 L                           V₂ = 125 L

T₁ = 300 °C                          T₂ = ? °C

P₁V₁ / T₁ = P₂V₂ / T₂                                               <----- Combined Law equation

(3.00 atm)(10.0 L) / (300 °C) = (1.00 atm)(125 L) / T₂         <----- Insert values

0.1 = (1.00 atm)(125 L) / T₂                                    <----- Simplify left side

0.1 = 125 / T₂                                                         <----- Multiply 1.00 and 125

0.1 x T₂ = 125                                                        <----- Multiply both sides by T₂

T₂ = 1,250                                                             <----- Divide both sides by 0.1