If I have 4.5 liters of gas at a temperature of 33 0C and a pressure of 6.54 atm, what will be the pressure of the gas if I raise the temperature to 94 0C and decrease the volume to 2.3 liters?

Respuesta :

This is an exercise in the general or combined gas law.

To start solving this exercise, we must obtain the following data:

Data:

  • V₁ = 4.5 l
  • T₁ = 33 °C + 273 = 306 k
  • P₁ = 6.54 atm
  • T₂ = 94 °C + 273 = 367 k
  • V₂ = 2.3 l
  • P₂ = ¿?

We use the following formula:

  • P₁V₁T₂ = P₂V₂T₁ ⇒ General Formula

Where

  • P₁ = Initial pressure
  • V₁ = Initial volume
  • T₂ = Initial temperature
  • P₂ = Final pressure
  • V₂ = Final volume
  • T₁ = Initial temperature

We clear the general formula for the final pressure.

[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{P_{1}V_{1}T_{2} }{V_{2}T_{1}} \ \to \ Clear \ formula \end{gathered}$}[/tex]

We solve by substituting our data in the formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{(6.54 \ atm)(4.5 \not{l})(367 \not{K}) }{(2.3 \not{l})(306 \not{k})} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{10800.81}{ 703.8 } \ atm \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf P_{2}=15.346 \ atm \end{gathered}$} }[/tex]

If I raise the temperature to 94°C and decrease the volume to 2.3 liters, the pressure of the gas will be 15,346 atm.

Answer:

15.35 atm

Explanation:

Combined Gas Law

[tex]\sf \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]

Temperature must be in kelvins (K).

To convert Celsius to kelvins, add 273.15.

Volume can be in any unit.

Given values:

  • P₁ = 6.54 atm
  • V₁ = 4.5 L
  • T₁ = 33 °C = 33 + 273.15 = 306.15 K
  • P₂ =
  • V₂ = 2.3 L
  • T₂ = 94 °C = 94 + 273.15 = 367.15 K

Rearrange the equation to isolate P₂:

[tex]\sf \implies P_2=\dfrac{P_1V_1T_2}{V_2T_1}[/tex]

Substitute the given values into the equation:

[tex]\sf \implies P_2=\dfrac{6.54 \cdot 4.5 \cdot 367.15}{2.3 \cdot 306.15}[/tex]

[tex]\sf \implies P_2=15.34516967[/tex]

Therefore, the pressure of the gas will be 15.35 atm (2 d.p.).

ACCESS MORE
EDU ACCESS