1. In an air-conditioned room at 19.0 C, a spherical balloon had the diameter of
ID: 900280 • Letter: 1
Question
1. 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 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.
2. 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 3.70 L ?
Explanation / Answer
Solution:
1.Given that pressure and nmber of moles remians constant.
Volume of a cube= radius^3= (50)3=125000, (51)^3=132651, T1=190 C=19+273=565
increase in volume is
V1 / T1 = V2 / T2 => T2= (V2/V1)*T1 => (132651/125000)*565=309.9K
the temperture outside the ballon =309.9K-273K= 36.9 C
2.given 2 grams of helium .
n1=moles of Helium = 2/4.003 =0.5 moles
n2=moles of Helium addes => to be calculated,
V1= 2.00L
V2= 3.00L
P1V1 / n1T1 = P2V2 / n2T2 given P is constant.T is constant
V1/n1=V2/n2 > plug in the values
2/0.5 =3.70/n2
=> n2= (3.70/2*0.5) => n2= 0.925 moles
moles= mass/molar mass => mass =moles *molar mass
Mass of helium = 0.925/4.003 =0.2315 grams
2.00 g-0.2315 = 1.8 grams of Helium was added
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