## Practice

To change a temperature expressed in degrees Celsius to a temperature on the Kelvin scale, what must be done to the Celsius temperature?

## Answer

add 273

Why must we use the Kelvin scale in gas law problems?

## Answer

so that no temperature has a negative value

To check your solutions to the problems, click the words Hint, Formula and Variables, and Answer.

The volume of a sample of gas is 2.00 L when the temperature is 11.0 °C. While the pressure remains constant, the temperature is changed to a new value, which causes the volume to become 3.00 L. What was the temperature changed to?

## Hint

Notice that the temperature given is in degrees Celsius. Kelvin temperatures must be used in all gas laws. This temperature must be converted to Kelvin by adding 273 to it.

## Formula and Variables

T_{1} = 11 °C + 273 = 284 K

V_{1} = 2.00 L

T_{2} = ?

V_{2} = 3.00 L

V_{1}T_{2} = V_{2}T_{1}

T_{2} = (V_{2}T_{1}) / V_{1}

## Answer

T_{2} = (3.00L x 284 K) / 2.00 L

T_{2} = 426 K

Which law was this an example of?

## answer

This is an example of Charles’ law

The volume occupied by a sample of gas is 480 mL when the pressure is 115 kPa. What pressure must be applied to the gas to make its volume become 650 mL?

Which law was this an example of?

## Formula and Variables

P_{1} = 115 kPa

V_{1} = 480 mL

P_{2} = ?

V_{2} = 650 mL

P_{1}V_{1} = P_{2}V_{2}

P_{2} = (P_{1}V_{1}) / V_{2}

## Answer

P_{2} = (P_{1}V_{1}) / V_{2}

P_{2} = (115 kPa x 480 mL) / 650 mL

P_{2} = 85 kPa

Which law was this an example of?

## Answer

This is an example of Boyle’s Law.

The volume occupied by a sample of gas is 240.0 mL when the pressure is 1.20 atm. What volume, at constant temperature, will the gas occupy when the pressure is decreased to 0.860 atm?

## Formula and Variables

P_{1} = 1.20 atm

V_{1} = 240.0 mL

P_{2} = 0.860 atm

V_{2} = ?

P_{1}V_{1} = P_{2}V_{2}

v_{2} = (P_{1}V_{1}) / P_{2}

## Answer

V_{2} = (P_{1}V_{1}) / P_{2}

V_{2} = (1.20 atm x 240.0 mL) / 0.860 atm

V_{2} = 335 mL

The volume of a sample of gas is 25.0 mL when the temperature is 270 K. If the temperature is changed to 30.0 °C, what will be the new volume occupied by the gas assuming that the pressure remains constant?

## Hint

Notice that the second temperature given is in degrees Celsius. Kelvin temperatures must be used in all gas laws. This temperature must be converted to Kelvin by adding 273 to it.

## Formula and Variables

T_{1} = 270 K

V_{1} = 25.0 mL

T_{2} = 30 °C + 273 = 293 K

V_{2} = ?

V_{1}T_{2} = V_{2}T_{1}

V_{2} = (V_{1}T_{2}) / T_{1}

## Answer

V_{2} = (V_{1}T_{2}) / T_{1}

V_{2} = (25.0 mL x 293 K) / 270 K

V_{2} = 28.1 mL

When the volume of a sample of gas is divided by the temperature of the gas, the result is 1.33 mL / K. The temperature of the gas is changed to a new value, which happens to be 411 K while the pressure is kept constant. What volume does the sample of gas occupy at 411 K?

## Note

Don’t confuse lowercase k, which refers to a constant value, with uppercase K, which refers to Kelvin.

## Formula and Variables

(V/T) = k

(V/T) = 1.33 mL/K

## Answer

V = 1.33 mL/K x 411 K

V = 547 mL

When the pressure exerted by a sample of gas is multiplied by the volume occupied by the sample, the result of this multiplication is 1.60 x 10^{5} mm Hg·mL. The pressure exerted by the sample changes to a new value, which happens to be 750 mm Hg. What volume will the sample occupy at this pressure, assuming that temperature remains constant?

## Formula and Variables

PV = k

## Answer

750 mm Hg x V = 1.60 x 10^{5} Hg x mL

V = (1.60 x 10^{5} mm Hg x mL) / 750 mm Hg

V = 213 mL