Answer :
The volume of sample when the gas is heated to 303 K is [tex]\boxed{{\text{(2)6}}{\text{.2 L}}}[/tex]
Further explanation:
Charles’s law:
Charles’s work showed that at constant pressure, the volume-temperature relationship for a fixed amount of gas is linear. In other words, Charles’s law can be stated that at constant pressure, the volume occupied by a fixed amount of a gas is directly proportional to its absolute temperature (Kelvin). This relationship is known as Charles’s law.
The mathematical representation of Charles’s law is,
[tex]{\mathbf{V}}\propto{\mathbf{T}}[/tex] [P and n are constant]
Where,
⦁ V is volume occupied by the fixed quantity of gas.
⦁ T is the temperature of a gas.
⦁ P is the pressure of a gas.
⦁ n denotes the number of moles of gas.
The relationship can also be expressed as,
[tex]\frac{{\text{V}}}{{\text{T}}} = {\text{constant}}[/tex] [P and n are constant]
Or it can also be expressed as follows:
[tex]\frac{{{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}} = \frac{{{{\text{V}}_{\text{2}}}}}{{{{\text{T}}_{\text{2}}}}}[/tex] …… (1)
Here,
[tex]{{\text{V}}_1}[/tex] is the initial volume of gas.
[tex]{{\text{V}}_2}[/tex] is the final volume of gas.
[tex]{{\text{T}}_1}[/tex] is the initial temperature of the gas.
[tex]{{\text{T}}_2}[/tex] is the final temperature of the gas.
Rearrange equation (1) to calculate [tex]{{\text{V}}_2}[/tex] .
[tex]{{\text{V}}_{\text{2}}} = \frac{{{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{2}}}}}{{{{\text{T}}_{\text{1}}}}}[/tex] …… (2)
The value of [tex]{{\text{V}}_1}[/tex] is 6 L.
The value of [tex]{{\text{T}}_1}[/tex] is 293 K.
The value of [tex]{{\text{T}}_2}[/tex] is 303 K.
Substitute these values in equation (2).
[tex]\begin{aligned}{{\text{V}}_{\text{2}}}&=\frac{{\left({{\text{6 L}}}\right)\left( {{\text{303 K}}}\right)}}{{\left( {{\text{293 K}}}\right)}}\\&={\text{6}}{\text{.20477 L}}\\&\approx{\mathbf{6}}{\mathbf{.2 L}}\\\end{aligned}[/tex]
So option (2) is the correct answer.
Learn more:
1. Law of conservation of matter states: https://brainly.com/question/2190120
2. Calculation of volume of gas: https://brainly.com/question/3636135
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: Charles’s law, volume, temperature, pressure, volume temperature relationship, absolute temperature, constant pressure, relationship, V directly proportional to T, ideal gas, ideal gas equation number of moles, moles, P, n, V, T, volume of gas, 6.2 L, 303 K, 293 K, 6 L.
The volume of the sample after the gas is heated to 303 K is 6.2 L
The correct answer to the question is Option (2) 6.2 L
From the question given above, the following data were obtained:
Initial volume (V₁) = 6 L
Initial temperature (T₁) = 293 K
Final temperature (T₂) = 303 K
Pressure = constant
Final volume (V₂) =?
Using the Charles' law equation, we can obtain the final volume of the gas as follow:
[tex]\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}\\\\\frac{6}{293} = \frac{V_{2}}{303}\\\\[/tex]
Cross multiply
293 × V₂ = 6 × 303
293 × V₂ = 1818
Divide both side by 293
[tex]V_{2} = \frac{1818}{293}\\\\[/tex]
V₂ = 6.2 L
Therefore, the volume of the sample after the gas is heated to 303 K is 6.2 L
The correct answer to the question is Option (2) 6.2 L
Learn more: https://brainly.com/question/16927784
