The CombinedGas Law : The CombinedGas Law
Manipulating Variables in equations : 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 : Multiplication and division We can do a similar operation with multiplication and division
E.g. 5x = 7, what does x equal?
We divide each side by 5 (to isolate x) …
5x/5 = 7/5 … x = 7/5 … x = 1.4
Alternatively, we can represent this as 5 moving to the other side of the equals sign …
5x = 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 : Multiplication and division Let’s look at a more complicated example: Isolate a in the equation:
Move b to the other side (from bottom to top) or Move 7 to the other side (from top to bottom)
Multiplication and division : Multiplication and division This time, isolate b in the equation: Move b to the other side (it must be on top) … Move everything to the other side of b Q - Rearrange the following equation to isolate each variable (you should have 6 equations)
Combined Gas Law Equations : Combined Gas Law Equations
Combining the gas laws : Combining the gas laws So far we have seen two gas laws: Jacques Charles Robert Boyle These are all subsets of a more encompassing law: the combined gas law Read pages 437, 438. Do Q 26 – 33 (skip 31) Joseph Louis Gay-Lussac
Q 26 : Q 26 V1 = 50.0 ml, P1 = 101 kPa
V2 = 12.5 mL, P2 = ? T1 = T2 Notice that T cancels out if T1 = T2
Slide 9 :
Slide 10 :
Q 27 : Q 27 V1 = 0.10 L, T1 = 298 K
V2 = ?, T2 = 463 P1 = P2 Notice that P cancels out if P1 = P2
Q 28 : Q 28 P1 = 150 kPa, T1 = 308 K
P2 = 250 kPa, T2 = ? V1 = V2 Notice that V cancels out if V1 = V2
Q 29 : Q 29 P1 = 100 kPa, V1 = 5.00 L, T1 = 293 K
P2 = 90 kPa, V2 = ?, T2 = 308 K Note: although kPa 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 : Q 30 P1 = 800 kPa, V1 = 1.0 L, T1 = 303 K
P2 = 100 kPa, V2 = ?, T2 = 298 K
Q 32 : Q 32 P1 = 6.5 atm, V1 = 2.0 mL, T1 = 283 K
P2 = 0.95 atm, V2 = ?, T2 = 297 K 33. The amount of gas (i.e. number of moles of gas) does not change. For more lessons, visit www.chalkbored.com