Chemistry questions - changes in volume, i really need your help pretty please?
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 1.75 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. Express your answer numerically in atmospheres.
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 51.0 cm 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 numerically in degrees Celsius.
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 3.10 L? (The temperature was held constant.) Express your answer numerically in grams.
please show me the working :(
a) Boyle's law : p1V1 = p2V2
1.75 x 3.00 = p2 x 1.00
p2 = 5.25 atm
r = 50/2 = 25 cm
V1 = 4 x 3.14 (25)^3/3=6.54 x 10^4 cm^3
r = 51/2=25.5 cm
V2 = 4 x 3.14 ( 25.5)^3/3 = 6.94 x 10^4 cm^3
T1 = 19 + 273 =292 K
V1/T1=V2/T2 ( Charles' law)
6.54 x 10^4 / 292 = 6.94 x 10^4 / T
T = 310 K=>37 °C
moles He = 2.00 g/ 4.00 g/mol= 0.500
2.00/ 3.10 = 0.500 / x
x = total moles He = 0.775
moles He added = 0.775 - 0.500=0.275
mass He added = 0.275 mol x 4.00 g/mol=1.10 g