The Combined Gas Law The Combined Gas Law
The Combined Gas Law
The Combined Gas Law Lesson Outcomes • ALL: - To be able to explain how the discoveries of several scientists were used to derive the combined gas law. • MOST: - To be able to use the combined gas law to complete calculations. • SOME: - To be able to explain how the Gas Law could be used in most situations and discuss the assumptions made about the ideal gas.
Manipulating Variables in equations • Often in an equation we want to isolate some variable, usually the unknown • From math: what ever you do to one side of an equation you have to do to the other side • Doing this keeps both sides the same • E. g. x + 5 = 7, what does x equal? • We subtract 5 from both sides … • x + 5 – 5 = 7 – 5, thus x = 2 • Alternatively, we can represent this as 5 moving to the other side of the equals sign … • x + 5 = 7 becomes x = 7 – 5 or x = 2 • Thus, for addition or subtraction, when you change sides you change signs
Multiplication and division • We can do a similar operation with multiplication and division • E. g. 5 x = 7, what does x equal? • We divide each side by 5 (to isolate x) … • 5 x/5 = 7/5 … x = 1. 4 • Alternatively, we can represent this as 5 moving to the other side of the equals sign … • 5 x = 7 becomes x = 7/5 • Thus, for multiplication and division, when you change sides you change position (top to bottom, bottom to top)
Multiplication and division • Let’s look at a more complicated example: (x) (y) 7 a = 5 b • Isolate a in the equation: • Move b to the other side (from bottom to top) (x) (y) 7 a = 5 b • Move 7 to the other side (from top to bottom) (x)(y)(b) 7 a = 5 (x)(y)(b) = a or a = (35) (5)(7)
Multiplication and division • This time, isolate b in the equation: (x) (y) 7 a = 5 b • Move b to the other side (it must be on top) … (x) (y) 7 a = 5 b • Move everything to the other side of b 35 a (b)(x)(y) 7 a b = = xy 5 Q - Rearrange the following P 1 V 1 P 2 V 2 equation to isolate each variable = T T 1 2 (you should have 6 equations)
Combined Gas Law Equations P 2 T 1 V 2 P 1 = T 2 V 1 T 1 P 1 T 2 V 1 = P 2 V 2 P 2 T 1 V 2 V 1 = T 2 P 1 P 1 T 2 V 1 P 2 = T 1 V 2 T 2 P 2 T 1 V 2 = P 1 V 1 P 1 T 2 V 1 V 2 = P 2 T 1
Combining the gas laws • So far we have seen two gas laws: Robert Boyle Jacques Charles Joseph Louis Gay-Lussac V 1 V 2 P 1 P 2 = = T 1 T 2 These are all subsets of a P V P 2 V 2 1 1 more encompassing law: = T 1 T 2 the combined gas law Read pages 437, 438. Do Q 26 – 33 (skip 31) P 1 V 1 = P 2 V 2
Q 26 V 1 = 50. 0 ml, P 1 = 101 k. Pa V 2 = 12. 5 m. L, P 2 = ? P 1 V 1 = T 1 (101 k. Pa)(50. 0 m. L) = (T 1) (P 2) = T 1 = T 2 P 2 V 2 T 2 (P 2)(12. 5 m. L) (T 2) (101 k. Pa)(50. 0 m. L)(T 2) (T 1)(12. 5 m. L) Notice that T cancels out if T 1 = T 2 = 404 k. Pa
Q 27 V 1 = 0. 10 L, T 1 = 298 K V 2 = ? , T 2 = 463 P 1 V 1 T 1 (P 1)(0. 10 L) (298 K) (V 2) = = P 1 = P 2 V 2 T 2 = (P 2)(V 2) (463) (P 1)(0. 10 L)(463 K) (P 2)(298 K) Notice that P cancels out if P 1 = P 2 = 0. 16 L
Q 28 P 1 = 150 k. Pa, T 1 = 308 K P 2 = 250 k. Pa, T 2 = ? P 1 V 1 T 1 (150 k. Pa)(V 1) (308 K) (T 2) = = = V 1 = V 2 P 2 V 2 T 2 (250 k. Pa)(V 2) (T 2) (250 k. Pa)(V 2)(308 K) (150 k. Pa)(V 1) Notice that V cancels out if V 1 = V 2 = 513 K = 240 °C
Q 29 P 1 = 100 k. Pa, V 1 = 5. 00 L, T 1 = 293 K P 2 = 90 k. Pa, V 2 = ? , T 2 = 308 K P 1 V 1 P 2 V 2 = T 1 T 2 (100 k. Pa)(5. 00 L) (90 k. Pa)(V 2) = (293 K) (308 K) (V 2) = (100 k. Pa)(5. 00 L)(308 K) = 5. 84 L (90 k. Pa)(293 K) Note: although k. Pa is used here, any unit for pressure will work, provided the same units are used throughout. The only unit that MUST be used is K for temperature.
Q 30 P 1 = 800 k. Pa, V 1 = 1. 0 L, T 1 = 303 K P 2 = 100 k. Pa, V 2 = ? , T 2 = 298 K P 1 V 1 = T 1 (800 k. Pa)(1. 0 L) = (303 K) (V 2) = P 2 V 2 T 2 (100 k. Pa)(V 2) (298 K) (800 k. Pa)(1. 0 L)(298 K) (100 k. Pa)(303 K) = 7. 9 L
Q 32 P 1 = 6. 5 atm, V 1 = 2. 0 m. L, T 1 = 283 K P 2 = 0. 95 atm, V 2 = ? , T 2 = 297 K P 1 V 1 = T 1 (6. 5 atm)(2. 0 m. L) = (283 K) P 2 V 2 T 2 (0. 95 atm)(V 2) (297 K) (6. 5 atm)(2. 0 m. L)(297 K) = 14 m. L (V 2) = (0. 95 atm)(283 K) 33. The amount of gas (i. e. number of moles of gas) does not change. For more lessons, visit www. chalkbored. com
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