# A gas occupies 246 mL at 567.3 Torr and 24.0 °C. When the pressure is changed to 771.0 Torr, what temperature is needed to maintain the same volume?

It's always a good idea to start with what you know.

You know that the volume of the container, which is given to you as

This means that only temperature and pressure will change.

When *volume* and *number of moles* are kept constant, pressure and temperature have direct relationship - this is known as Gay Lussac's Law.

In other words, if pressure increases, temperature increases as well. If pressure decreases, temperature decreases as well.

Mathematically, this is written as

#P_1/T_1 = P_2/T_2" "# , where

#P_1# ,#T_1# - the pressure and temperature of the gas at an initial state;

#P_2# ,#T_2# - the pressure and temperature of the gas at a final state.In your case, you know that the pressue is

increasingfrom#"567.3 torr"# , to#"771.0 torr"# . This means that you can expect the needed temperature to be higher than the initial#24.0^@"C"# .Plug in your values and solve for

#T_2#

#T_2 = P_2/P_1 * T_1#

#T_2 = (771.0color(red)(cancel(color(black)("torr"))))/(567.3color(red)(cancel(color(black)("torr")))) * 24.0^@"C" = color(green)(32.6^@"C")# As predict, the temperature must be higher than what it initially was.

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To maintain the same volume when the pressure changes from 567.3 Torr to 771.0 Torr, we can use the combined gas law equation:

P1V1/T1 = P2V2/T2

Given: P1 = 567.3 Torr V1 = 246 mL P2 = 771.0 Torr V2 = 246 mL

We can rearrange the equation to solve for T2:

T2 = (P2 * V1 * T1) / (P1 * V2)

Substituting the given values:

T2 = (771.0 Torr * 246 mL * 24.0 °C) / (567.3 Torr * 246 mL)

T2 ≈ 41.8 °C

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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