Question

Gas law help?

1) A weather balloon is released on a warm summer day (30 C) containing 15L of air at 1 atm. Assuming the pressure inside the balloon does not change and the balloon rises in the air and cools in the upper atmosphere to 18 C what is the new volume of the balloon?

2)A 3L flask of Hydrogen at a pressure of 1 atm and a temperature of 30 C is stored in the flatbed of a truck. R value is .0821. How many moles are present in the flask?

Answer 1

1) `V=14.406 L`
2) `n=0.12 " mol"`

Explanation:

1)
`T_0=30°C`
`V_a=15 L`
`p_0=1" atm"`
`T_1=18 °C`

`p V=m/M R T => V=m/M (R T_1)/p_0`
Calculate `m` from the gas law and initial value:
`m=(p_0 V_a M)/(R T_0)`
`V=(p_0 V_a M)/(M R T_0) (R T_1)/p_0=V_a T_1/T_0`

Or use Charles's law: `V/T=const.`
`V_a/T_0=V/T_1 => V=V_a T_1/T_0`
`V=14.406 L`

2)
`p=1 "atm"`
`T=30°C`
`V=3 L`
`p V=n R T => n=(p V)/(R T)=(1 "atm"xx 3 L)/(0.0821 (L" atm")/(K "mol") (273+30)K)=0.12 " mol"`