t Deriving Gas Law Formulas Learning Goal: To understand how to determine the appropriate formula for a given gas law problem. When you are unsure of which formula to use to solve a gas law problem, it is often helpful to make a chart of initial and final values of pressure P volume V, number of moles, n, and temperature T, as shown in the table Initial Final This type of chart will help you to determine which quantities are changing and which quantities remain the same. For example, use the formula Ph Vi PrV2 for the product of pressure and volume at two different points in time when pressure and volume are changing but the number of moles of gas and the temperature are constant. Here is how this formula is derived from the ideal gas law, PV nRT: 1. If n and T are constant, the entire quantity nRT is constant. 2. Therefore, PV is constant. 3. It follows that the quantity PV at any point in time will be the same value as at any other point in time. 4. Therefore Ph Vi 2 V2 Now imagine an experiment where your chart looks like this Initial Final P 2 atm 2 atm V 1.7 L 2.5 L m 0.45 mol 0.45 mol T 273 K It is clear that V and T are the quantities that are changing, while Pand n are constant. To put a constants P, n, and R ogether, we need to do a little bit of algebra: n RT 2. TV 4. T s constant. 5. Therefore the quantity V/T at any point in time will be the same value as at any other point in time, so
The ideal gas law (PV=nRT) describes the relationship among pressure P, volume V, temperature T, and molar amount n. When some of these variables are constant, the ideal gas law can be rearranged in different ways to take the following forms where k is a constant:
Name
Expression
Constant
Boyle's law
PV=nRT=k
n and T
Charles's law
VT=nRP=k
n and P
Avogadro's law
Vn=RTP=k
T and P
Part A
A certain amount of chlorine gas was placed inside a cylinder with a movable piston at one end. The initial volume was 3.00 L and the initial pressure of chlorine was 1.15 atm . The piston was pushed down to change the volume to 1.00 L. Calculate the final pressure of the gas if the temperature and number of moles of chlorine remain constant.. (Figure 1)
Express your answer with the appropriate units.
Pfinal =
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Part B
In an air-conditioned room at 19.0 âC, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius? Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.
Express your answer with the appropriate units.
outside temperature =
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Part C
A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 4.10 L ? (The temperature was held constant.)