Question

A gas sample occupies 3.50 liters of volume at 20.°c. what volume will this gas occupy at 100.°c (reported to three significant figures?

Answer 1

Explanation:

According to Charle's law, at constant pressure the volume of an ideal gas is directly proportional to the temperature.

That is,             $Volume \propto Temperature$

Hence, it is given that $V_{1}$ is 3.50 liters, $T_{1}$ is 20 degree celsius, and $T_{2}$ is 100 degree celsius.

Therefore, calculate $V_{2}$ as follows.

                           $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

                           $\frac{3.50 liter}{20^{o}C} = \frac{V_{2}}{100^{o}C}$

                                $V_{2}$ = 17.5 liter

Thus, we can conclude that volume of gas required at 100 degree celsius is 17.5 liter.

Answer 2

The volume of the gas at ${\text{100 }}^\circ{\text{C}}$ is $\boxed{{\text{17}}{\text{.5 L}}}$

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,

${\mathbf{V}}\propto{\mathbf{T}}$                                             [P and n are constant]

Here,

 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,

$\frac{{\text{V}}}{{\text{T}}}={\text{constant}}$                               [P and n are constant]

Or it can also be expressed as follows:

$\frac{{{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}}=\frac{{{{\text{V}}_{\text{2}}}}}{{{{\text{T}}_{\text{2}}}}}$                          …… (1)

Here,

${{\text{V}}_1}$ is the initial volume of gas.

${{\text{V}}_2}$ is the final volume of gas.

${{\text{T}}_1}$ is the initial temperature of the gas.

${{\text{T}}_2}$ is the final temperature of the gas.

Rearrange equation (1) to calculate ${{\text{V}}_2}$.

${{\text{V}}_{\text{2}}}=\frac{{{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{2}}}}}{{{{\text{T}}_{\text{1}}}}}$                           …… (2)

The value of ${{\text{V}}_1}$ is 3.50 L.

The value of ${{\text{T}}_1}$ is ${\text{20 }}^\circ{\text{C}}$.

The value of ${{\text{T}}_2}$ is ${\text{100 }}^\circ{\text{C}}$.

Substitute these values in equation (2).

$\begin{gathered}{{\text{V}}_{\text{2}}}=\frac{{\left({{\text{3}}{\text{.50 L}}}\right)\left({{\text{100 }}^\circ{\text{C}}}\right)}}{{\left({{\text{20 }}^\circ{\text{C}}}\right)}}\\={\mathbf{17}}{\mathbf{.5 L}}\\\end{gathered}$

The volume of gas occupied at${\mathbf{100 ^\circ C}}$is 17.5 L.

Learn more:

1. Law of conservation of matter states: brainly.com/question/2190120

2. Calculation of volume of g as: brainly.com/question/3636135

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Ideal gas of 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, 17.5 L, Kelvin, 3.50 L,