Respuesta :
From the gas laws, Charles law states that the volume of a fixed mas of a gas is directly proportional to absolute temperature at constant pressure.
and Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to pressure at constant temperature, therefore combining the two we have, PV/T, for two gases we have,
P1V1/T1=P2V2/T2
V1 = 425 ml, T1= 35 +273 =308 K, P1= 805.2 torr
V2 = ? and T2 = 23 +273 = 296K, P2 = 784.1torr
V2 = P1V1T2/P2T1
= (805.2×425×296)/784×308
= 419.486 ml
= 419.5 ml
and Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to pressure at constant temperature, therefore combining the two we have, PV/T, for two gases we have,
P1V1/T1=P2V2/T2
V1 = 425 ml, T1= 35 +273 =308 K, P1= 805.2 torr
V2 = ? and T2 = 23 +273 = 296K, P2 = 784.1torr
V2 = P1V1T2/P2T1
= (805.2×425×296)/784×308
= 419.486 ml
= 419.5 ml
Volume of hydrogen sample at [tex]23^\circ\text{C}[/tex] is [tex]\boxed{419.4\text{ mL}}[/tex].
Further Explanation:
Ideal gas equation:
A hypothetical gas comprising of many randomly moving particles having perfectly elastic collisions between them is called ideal gas. The expression for ideal gas equation is mentioned below.
[tex]\text{PV}=\text{nRT}[/tex] ...... (1)
Here,
P is the pressure of gas.
V is the volume of gas.
T is the absolute temperature of gas.
n is the number of moles of gas.
R is the universal gas constant.
At temperature [tex]\text{T}_{1}[/tex] , volume [tex]\text{V}_{1}[/tex] and pressure [tex]\text{P}_{1}[/tex] , ideal gas equation for hydrogen gas modifies as follows:
[tex]\text{P}_{1}\text{V}_{1}=\text{nRT}_{1}[/tex] ...... (2)
At temperature [tex]\text{T}_{2}[/tex] , volume [tex]\text{V}_{2}[/tex] and pressure [tex]\text{P}_{2}[/tex] , ideal gas equation for hydrogen gas modifies as follows:
[tex]\text{P}_{2}\text{V}_{2}=\text{nRT}_{2}[/tex] ...... (3)
Dividing equation (3) by equation (2),
[tex]\dfrac{\text{P}_{2}\text{V}_{2}}{\text{P}_{1}\text{V}_{1}}=\dfrac{\text{T}_{2}}{\text{T}_{1}}[/tex] ...... (4)
Rearrange equation (4) to calculate .
[tex]\text{V}_{2}=\dfrac{{\text{P}_{1}\text{V}_{1}\text{T}_{2}}}{\text{P}_{2}\text{T}_{1}}[/tex] …… (5)
The value of [tex]\text{P}_{1}[/tex] can be calculated as follows:
[tex]\begin{aligned}\text{P}_{1}=&763\text{ torr}+42.2\text{ torr}\\=&805.2\text{ torr}\end{aligned}[/tex]
The value of [tex]\text{P}_{2}[/tex] can be calculated as follows:
[tex]\begin{aligned}\text{P}_{2}=&763\text{ torr}+21.1\text{ torr}\\=&784.1\text{ torr}\end{aligned}[/tex]
The value of [tex]\text{T}_1[/tex] can be calculated as follows
[tex]\begin{aligned}\text{T}_1=&\left(35+273.15\right)\text{ K}\\=&\ 308.15\text{ K}\end{aligned}[/tex]
The value of [tex]\text{T}_2[/tex] can be calculated as follows
[tex]\begin{aligned}\text{T}_2=&\left(23+273.15\right)\text{ K}\\=&\ 296.15\text{ K}\end{aligned}[/tex]
Substitute 805.2 torr for [tex]\text{P}_{1}[/tex] , 425 mL for [tex]\text{V}_{1}[/tex] , 784.1 torr for [tex]\text{P}_{2}[/tex] , 308.15 K for [tex]\text{T}_{1}[/tex] and 296.15 K for [tex]\text{T}_{2}[/tex] in equation (5).
[tex]\begin{aligned}\text{V}_{2}&=\dfrac{\left({805.2\text{ torr}\right)\left(425\text{ mL}\right)\left(296.15\text{ K}\right)}}{\left(784.1\text{ torr}\right)\left(308.15\text{ K}\right)}\\&=419.4\text{ mL}\end{aligned}[/tex]
Therefore volume of hydrogen sample at [tex]23^\circ\text{ C}[/tex] comes out to be 419.4 mL.
Learn more:
1. Which statement is true for Boyle’s law? https://brainly.com/question/1158880
2. Calculation of volume of gas: https://brainly.com/question/3636135
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: ideal gas equation, R, T, n, P, V, T1, T2, P1, P2, V1, V2, 419.4 mL, pressure, volume, universal gas constant.
