Respuesta :
Answer: The change in volume is 1.52 L
Explanation:
According to ideal gas equation:
[tex]PV=nRT[/tex]
P = pressure of gas = 0.96 atm
V = Volume of gas = ?
n = number of moles
R = gas constant =[tex]0.0821Latm/Kmol[/tex]
T =temperature =[tex]18^0C=(18+273)K=291K[/tex]
[tex]V=\frac{nRT}{P}[/tex]
[tex]V=\frac{0.25mol\times 0.0820 L atm/K mol\times 291K}{0.799atm}=7.47L[/tex]
The combined gas equation is,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = 0.799 atm
[tex]P_2[/tex] = final pressure of gas = 1.11 atm
[tex]V_1[/tex] = initial volume of gas = 7.47 L
[tex]V_2[/tex] = final volume of gas = ?
[tex]T_1[/tex] = initial temperature of gas = [tex]18^0C=(18+273)K=291K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]49^0C=(49+273)K=322K[/tex]
Now put all the given values in the above equation, we get:
[tex]\frac{0.799\times 7.47}{291}=\frac{1.11\times V_2}{322}[/tex]
[tex]V_2=5.95L[/tex]
The change in volume = (7.47 - 5.95)L=1.52 L
The space occupied by the substance, solution or particle in a system is called volume. The change in volume of the neon gas is 1.52 L.
What is the ideal gas equation?
The ideal gas equation is the equation that states the relation between the pressure, volume, temperature, moles and gas constant of the hypothetical gas.
The ideal gas equation of a hypothetical ideal gas can be given as,
[tex]\rm PV = nRT[/tex]
Where,
- Pressure (P) of the gas = 0.96 atm
- The volume of the gas = V
- Number of moles (n) = 0.25 mol
- Gas constant (R) = 0.0821 Latm/ Kmol
- Temperature (T) = 291 K
From the above equation volume can be calculated as,
[tex]\begin{aligned} \rm V &= \rm \dfrac{nRT}{P}\\\\&= \dfrac{0.25 \times 0.0820 \times 291}{0.799}\\\\&= 7.47 \;\rm L\end{aligned}[/tex]
The combined gas equation can be shown as,
[tex]\rm \dfrac{P_{1}V_{1}}{T_{1}} = \dfrac{P_{2}V_{2}}{T_{2}}[/tex]
Where,
- The initial pressure of the gas [tex]\rm (P_{1})[/tex] = 0.799 atm
- The final pressure of the gas [tex]\rm (P_{2})[/tex] = 1.11 atm
- The initial volume of gas [tex]\rm (V_{1})[/tex] = 7.47 L
- The final volume of gas [tex]\rm (V_{2})[/tex] = ?
- The initial temperature of the gas [tex]\rm (T_{1})[/tex] = 291 K
- The final temperature of the gas [tex]\rm (T_{2})[/tex] = 322 K
Substituting values in the above equation:
[tex]\begin{aligned}\dfrac{0.799 \times 7.47}{291} &= \rm \dfrac{1.11 \times V_{2}}{322}\\\\&= 5.95 \;\rm L\end{aligned}[/tex]
Volume change of the gas is, [tex](7.47 - 5.95)\;\rm L = 1.52\;\rm L[/tex]
Therefore the change in the volume of the neon gas is 1.52 L.
Learn more about the ideal gas equation here:
https://brainly.com/question/80015
