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Chapter 8: Q. 8.41 (page 273)

Rearrange the variable in the combined gas law to solve for $T_{2}$ .

Short Answer

Expert verified

The combined gas law for $T_{2}$ is role="math" localid="1652612034505" $T_{2} = \frac{T_{1} 脳 P_{2} 脳 V_{2}}{P_{1} 脳 V_{1}}$ .

Step by step solution

01

Given Information

We need to rearrange the variable in combined gas law to solve for $T_{2}$

02

Simplify

The combined gas law is given as:

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

Here,

$P_{1}$ is initial pressure,

$T_{2}$ is initial temperature,

role="math" localid="1652611570206" $V_{1}$ is initial volume,

$P_{2}$ is final pressure,

role="math" localid="1652611612307" $T_{2}$ is final temperature and

$V_{2}$ is the final volume.

Now, in case if are asked to find the final temperature the combined gas equation will be rearranged as:

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

For $T_{2}$ is equal to:

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

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Most popular questions from this chapter

Calculate the final temperature, in degrees Celsius, for each of the following, if $V, n$ do not change:

a. A sample of helium gas with a pressure of role="math" localid="1652606588066" $250 T o r r$ at $0 掳 C$ is heated to give a pressure of role="math" localid="1652606595080" $1500 T o r r$ .

b. A sample of air atrole="math" localid="1652606709077" $40 掳 C$ and $740 m m H g$ is cooled to give a pressure of $680 m m H g .$

A gas sample has a pressure of $2.35 a t m$ when the temperature is $- 15 掳 C$ . What is the final pressure, in atmospheres, when the temperature is $46 掳 C$ , with no change in the volume or amount of gas?

Indicate which diagram $(1, 2 o r 3)$ represents the volume of the gas sample in a flexible container when each of the following changes $(a t o b)$ takes place: $(8.2, 8.3)$

a. Temperature increases if the pressure does not change.

b. Temperature decreases if the pressure does not change.

c. Atmospheric pressure decreases if the temperature does not change.

d. Doubling the atmospheric pressure and doubling the Kelvin temperature.

A balloon is filled with helium gas at a partial pressure of $1.00 a t m$ and neon gas with a partial pressure of $0.50 a t m$ . For each of the following changes (a to e) of the initial balloon, select the diagram (A, B, or C) that shows the final volume of the balloon: $(8.2, 8.3, 8.6)$

a. The balloon is put in a cold storage unit ( $P a n d n$ do not change).

b. The balloon floats to a higher altitude where the pressure is less ( $n a n d T$ do not change).

c. All of the neon gas is removed ( $T a n d P$ do not change).

d. The Kelvin temperature doubles and half of the gas atoms leak out ( $P$ does not change).

e. $2.0 m o l e s o f O_{2}$ gas is added ( $T a n d P$ do not change).

A gas with a volume of 4.0 L is in a closed container. Indicate the changes (increases, decreases, does not change) in pressure when the volume undergoes the following changes at constant temperature and amount of gas:
a. The volume is compressed to $2.0$ L.
b. The volume expands to $12$ L.
c. The volume is compressed to $0.40$ L

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