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

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 constant: In an air-conditioned room at 19.0 degree 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 in degrees Celsius? Assume that the balloon is a perfect sheer and the pressure and the number of moles of air molecules remained the same. A cylinder with a movable piston contains 2.00g 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 changed form 2.00 L to 2.90 L?

Explanation / Answer

C)

Since pressure is constant.
we need to use:
Vi/ni = Vf/nf

Here V is nor volume and n is for number of moles

Vi = 2 L
Vf = 2.9 L
molar mass of He = 4 g/mol
ni = mass/ molar mass of He
     = 2/4
     = 0.5 mol

use:
Vi/ni = Vf/nf
2/0.5 = 2.9/nf
nf= 0.725 mol

Final mass of He = nf*molar mass
                                  = 0.725* 4
                                   = 2.9 g

Mass of Helium added = final mass - initial mass
                                               =2.9 g - 2 g
                                               = 0.9 g

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