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The Gas Laws

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**Boyle’s Law: Pressure and Volume**

If the temperature is constant, as the pressure of a gas increases, the volume decreases. In turn, as the pressure decreases, the volume increases.

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**Boyle’s Law: Pressure and Volume**

Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. P1 x V1 = P2 x V2 P = pressure V = volume

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Using Boyle’s Law A balloon contains 30L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25 kPa? Step 1: use Boyle’s law: P1 x V1 = P2 x V2

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**Using Boyle’s Law Step 2: set up equation to solve for V2**

V2 = (V1 x P1) / P2 Step 3: plug and chug V2 = (30L x 103 kPa) / 25 kPa V2 = 124 L

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**Using Boyle’s Law Practice**

1. Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.5 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?

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**Using Boyle’s Law Practice**

2. A gas with a volume of 4 L at a pressure of 205 kPa is allowed to expand to a volume of 12 L. What is the pressure in the container if the temperature remains constant?

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**Charles’s Law: Temperature and Volume**

As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant.

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**Charles’s Law: Temperature and Volume**

Charles’s law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. V1/T1 = V2/T2

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Using Charles’s Law A balloon inflated in a room at 24 °C has a volume of 4 L. The balloon is then heated to a temperature of 58 °C. What is the new volume if the pressure remains constant? Step 1: Turn Celsius into Kelvin K = C + 273 = 297 K for T1 = 331 K for T2

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**Using Charles’s Law Step 2: rearrange Charles’s law to isolate V2**

V2 = (V1 x T2) / T1 Step 3: plug and chug V2 = (4L x 331K) / 297K = 4.46 L

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**Using Charles’s Law Practice**

3. If a sample of gas occupies 6.8 L at 325°C, what will its volume be at 25°C if the pressure does not change?

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**Using Charles’s Law Practice**

4. Exactly 5L of air at -50 °C is warmed to 100 °C. What is the new volume if the pressure remains constant?

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**Gay-Lussac’s Law: Pressure and Temperature**

As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant.

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**Gay-Lussac’s Law: Pressure and Temperature**

Gay-Lussac’s law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant. P1/T1 = P2/T2

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**Using Gay-Lussac’s Law**

The gas in a used aerosol can is at a pressure of 103kPac at 25°C. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928°C? Step 1: turn celsius into kelvin = 298 K = 1201 K

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**Using Gay-Lussac’s Law**

Step 2: Use Gay-Lussac’s law and isolate P2 P2 = (P1 x T2) / T1 Step 3: Plug and chug P2 = (103 kPa x 1201 K) / 298 K = 415 kPa

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**Using Gay-Lussac’s Law Practice**

5. The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire?

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**Using Gay-Lussac’s Law Practice**

6. a sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K?

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The Combined Gas Law The combined gas law describes the relationship among the pressure, temperature, and volume of an enclosed gas.

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The Combined Gas Law The combined gas law allows you to do calculations for situations in which only the amount of gas is constant. P1 x (V1/T1) = P2 x (V2/T2)

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**Using The Combined Gas Law**

The volume of a gas filled balloon is 30L at 313 K and 153 kPa pressure. What would the volume be at standard temperature and pressure (STP)? Step 1: Realize that T2 = 273K and P2 = kPa because they are at STP.

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**Using The Combined Gas Law**

Step 2: Rearrange the combined gas law to isolate V2: V2 = (V1 x P1 x T2) / (P2 x T1) Step 3: Plug and Chug V2 = (30L x 153kPa x 273K) / (101.3kPa x 313K) V2 = 39.5 L

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**Combined Gas Law Practice**

7. A gas at 155 kPa and 25°C has an initial volume of 1L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125°C. What is the new volume?

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**Combined Gas Law Practice**

8. A 5L air sample has a pressure of 107kPa at a temperature of 250°C. If the temperature is raised to 102°C and the volume expands to 7L, what will the new pressure be?

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