Add to table of contents: Com & Ideal problemsPg. 62 Combined & Ideal Gas LawsPg. 63

Combined and Ideal Gas Laws Pg. 63

3 The Combined Gas Law Boyle’s law shows the relationship between pressure and volume. – At constant temperature. Charles’s law shows the relationship between volume and absolute temperature. – At constant pressure. The two laws can be combined together to give a law that predicts what happens to the volume of a sample of gas when both the pressure and temperature change. – As long as the amount of gas stays constant.

T(K) = t(°C) + 273, Example 11.4—A Sample of Gas Has an Initial Volume of 158 mL at a Pressure of 735 mmHg and a Temperature of 34 °C. If the Gas Is Compressed to 108 mL and Heated to 85 °C, What Is the Final Pressure? Since T increases and V decreases we expect the pressure should increase, and it does. V 1 = 158 mL, t 1 = 34 °C L, P 1 = 735 mmHg V 2 = 108 mL, t 2 = 85 °C P 2, mmHg Check: Solution: Solution Map: Relationships: Given: Find: P 1,V 1, V 2, T 1, T 2 P2P2 4

5 Practice—A Gas Occupies 10.0 L When Its Pressure Is 3.00 atm and Temperature Is 27 °C. What Volume Will the Gas Occupy Under Standard Conditions?

T(K) = t(°C) + 273, Practice—A Gas Occupies 10.0 L When Its Pressure Is 3.00 Atm and Temperature Is 27 °C. What Volume Will the Gas Occupy Under Standard Conditions?, Continued When T decreases, V should decrease; when P decreases, V should increase—opposite trends make it hard to evaluate our answer. V 1 = 10.0 L, t 1 = 27 °C L, P 1 = 3.00 atm t 2 = 0 °C, P 2 = 1.00 atm V 2, L Check: Solution: Solution Map: Relationships: Given: Find: V 1, P 1,P 2, T 1, T 2 V2V2 6

7 Avogadro’s Law Volume is directly proportional to the number of gas molecules. – V = constant x n. – Constant P and T. – More gas molecules = larger volume. Count number of gas molecules by moles, n. Equal volumes of gases contain equal numbers of molecules. – The gas doesn’t matter.

8 Avogadro’s Law, Continued

mol added = n 2 – n 1, Example 11.5—A 0.22 Mol Sample of He Has a Volume of 4.8 L. How Many Moles Must Be Added to Give 6.4 L? Since n and V are directly proportional, when the volume increases, the moles should increase, and it does. V 1 =4.8 L, V 2 = 6.4 L, n 1 = 0.22 mol n 2, and added moles Check: Solution: Solution Map: Relationships: Given: Find: V 1, V 2, n 1 n2n2 9

10 Practice—If 1.00 Mole of a Gas Occupies 22.4 L at STP, What Volume Would Moles Occupy?

Practice—If 1.00 Mole of a Gas Occupies 22.4 L at STP, What Volume Would Moles Occupy?, Continued Since n and V are directly proportional, when the moles decreases, the volume should decrease, and it does. V 1 =22.4 L, n 1 = 1.00 mol, n 2 = mol V2V2 Check: Solution: Solution Map: Relationships: Given: Find: V 1, n 1, n 2 V2V2 11

12 Ideal Gas Law By combining the gas laws, we can write a general equation. R is called the Gas Constant. The value of R depends on the units of P and V. – We will use and convert P to atm and V to L. Use the Ideal Gas Law when you have a gas at one condition, use the Combined Gas Law when you have a gas whose condition is changing.

1 atm = 14.7 psi T(K) = t(°C) Example 11.7—How Many Moles of Gas Are in a Basketball with Total Pressure 24.2 Psi, Volume of 3.2 L at 25 °C? 1 mole at STP occupies 22.4 L at STP; since there is a much smaller volume than 22.4 L, we expect less than 1 mole of gas. V = 3.2 L, P = 24.2 psi, t = 25 °C, n, mol Check: Solution: Solution Map: Relationships: Given: Find: P, V, T, Rn 13

Practice—Calculate the Volume Occupied by 637 g of SO 2 (MM 64.07) at 6.08 x 10 3 mmHg and –23 °C. 14

1 atm = 760 mmHg T(K) = t(°C) + 273, 1 mol SO 2 = g Practice—Calculate the Volume Occupied by 637 g of SO 2 (MM 64.07) at 6.08 x 10 3 mmHg and –23 °C, Continued. m SO2 = 637 g, P = 6.08 x 10 3 mmHg, t = −23 °C, V, L Solution: Solution Map: Relationships: Given: Find: P, n, T, RVgn 15