1. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 6 Gases 6.6 The Combined Gas Law 1

2. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. The Combined Gas Law The combined gas law uses Boyle’s law, Charles’s law, and Gay-Lussac’s law (n is constant). P 1 V 1 =P 2 V 2 T 1 T 2 2

3. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Summary of Gas Laws 3

4. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35  C and 0.850 atm pressure. What is the volume (mL) of the gas at −95  C and a pressure of 802 mmHg (n constant)? Step 1Organize the data into a table of initial and final conditions Conditions Initial Final T 1 = 35  C + 273 T 2 = −95  C + 273 = 308 K = 178 K V 1 = 675 mL V 2 = ? P 1 = 646 mmHg P 2 = 802 mmHg 4

5. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35  C and 0.850 atm pressure. What is the volume (mL) of the gas at −95  C and a pressure of 802 mmHg (n constant)? Step 2 Rearrange to solve for unknown quantity: V 2 P 1 V 1 = P 2 V 2 T 1 T 2 V 2 = V 1  P 1  T 2 P 2  T 1 5

6. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35  C and 0.850 atm pressure. What is the volume (mL) of the gas at −95  C and a pressure of 802 mmHg (n constant)? Step 3 Substitute the values into the gas law equation and calculate. V 2 = 675 mL  646 mmHg  178 K = 314 mL 802 mmHg  308 K 6

7. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29  C. At what temperature (  C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n is constant)? 7

8. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Step 1 Organize the data into a table of initial and final conditions. Conditions Initial Final P 1 = 0.800 atm P 2 = 3.20 atm V 1 = 0.180 L V 2 = 90.0 mL (180 mL) T 1 = 29  C + 273 T 2 = ? = 302 K Be sure to use the Kelvin (K) temperature in gas calculations. 8

9. Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Step 2 Rearrange to solve for unknown quantity: T 2 P 1 V 1 = P 2 V 2 and T 2 = T 1  P 2  V 2 T 1 T 2 P 1  V 1 Step 3 Substitute the values into the gas law equation and calculate. T 2 = 302 K  3.20 atm  90.0 mL = 604 K 0.800 atm  180.0 mL T 2 = 604 K − 273 = 331  C 9