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?

1 Answer

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"#