Agas-filled weather balloon has a volume of 53.0 l at ground level, where the pressure is 751 mmhg and the temperature is 25.0 °c. after being released, the balloon rises to an altitude where the temperature is –2.01 °c and the pressure is 0.511 atm. what is the weather balloon's volume at the higher altitude?

The volume at the higher altitude is 8.14L

Explanation:

In this problem we need to use the Ideal Gas Law, which is expressed like this:

Where is the pressure, is the volume, is the number of molecules, is the ideal gas constant and is the temperature.

Now, we need to apply the Ideal Gas Law to each case, at ground level and at the higher altitude.

At ground level:

Then, we will isolate , to use it later:

At higher altitude:

Now, we combined both equation, because is the same in both cases:

The problem asks about , so we isolate that volume and replace all known variables:

If we transform that volume into litres, we know that 1 litre is :

Therefore, the volume at the higher altitude is 8.14L

We know from gas equation: 
PV=mRT
Where:P is pressure (1 torr = 0.013N/cm2)V is the volume of the balloonm is the mass of gas in the balloon (constant) R is universal gas constant divided by mean molar wt of air (about 28 g/mol) T is thermodynamic temperature (T in Kelvin; T=273 + t (in deg C)

P1 * V1 =m*R*T1 (i) 
P2 * V2 =m*R*T2 (ii)

Dividing 1 by 2 we get: 

V1 / V2 = (P2/P1) * (T1/T2)

Given:
V1=53, P1 = 751, T1 = 273+25=298
V2=?, P2 = 0.511=388.36mmhg, T2 = 273+(-2.01)=271

so, V2 = 53*(751/0.511)*(271/298) = 70835.0057mm^3
 

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Iwould have to say sorry i can't elaborate more. hope this though!