The ideal gas law (PV=nRT) describes the relationship among pressure P, volume V

Question

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 1.80atm . 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 =

Part B

In an air-conditioned room at 19.0 C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0cm in diameter. What was the temperature outside? 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 =

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 4.50L ? (The temperature was held constant.) Express your answer with the appropriate units. mass of helium added =

Explanation / Answer

A)

Since,he temperature and number of moles of chlorine remain constant

Then,

P1V1 = P2V2

3 * 1.80 = Pfinal * 1.00

Hence, Pfinal = 5.40 atm.

B)

   Since,the pressure and number of moles of air molecules remains the same

V1/T1 = V2/T2

(4/3*pi*r13) / 19 = (4/3*pi*r23) / T2

r13/19 = r23/T2

T2 = ((51^3)*2*(273+19))/(2*(50^3)) = 309.87 K

Hence,  the temperature outside = 309.87 - 273 = 36.87? oC

C)

Here, pressure and temprature is constant

So,

V1/n1 = V2/n2

2/(2/4) = 4.5/ ( m/4)

m = 4.5 * 2 / 2 = 4.5

  Grams of helium were added to the cylinder = 4.5 - 2 = 2.5 grams

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