Question

choose the correct set of variables to solve the following problem: what is the volume of a balloon if it contains 3.2 moles of helium at a temperature of 20°c and 1.2 atm?
p = x (unknown), v = 3.2, mol, n = 1.2 atm, t = 20°c k
p = 1.2 atm, v = x (unknown), n = 3.2 mol, t = 293 k
p = 293 k, v = 3.2 mol, n = x (unknown), t = 1.2 atm
p = 1.2 atm, v = 3.2 mol, n = 20°c, t = x (unknown)

Explanation:

Step1: Recall the Ideal Gas Law

The Ideal Gas Law is \(PV = nRT\). Here, we need to find the volume \(V\) of a balloon containing \(n = 3.2\) moles of helium at \(P=1.2\) atm and \(T = 20^{\circ}C\). First, convert temperature to Kelvin: \(T=(20 + 273)K=293K\).

Step2: Analyze each option

• First option: \(P=x\) (unknown), \(V = 3.2\), \(n=1.2\) atm, \(T = 20^{\circ}C\). The units of \(n\) (should be mol, here it's atm) and the assignment of known - unknown variables are wrong.
• Second option: \(P = 1.2\) atm, \(V=x\) (unknown), \(n = 3.2\) mol, \(T = 293K\). This correctly assigns \(P = 1.2\) atm (known), \(V\) (unknown as we need to find volume), \(n = 3.2\) mol (given), and \(T=293K\) (converted from \(20^{\circ}C\)).
• Third option: \(P = 293K\), \(V = 3.2\) mol, \(n=x\) (unknown), \(T = 1.2\). Units are mismatched (\(P\) has unit of \(K\), \(V\) has unit of mol).
• Fourth option: \(P = 1.2\) atm, \(V = 3.2\) mol, \(n = 20^{\circ}C\), \(T=x\) (unknown). Units are wrong (\(V\) has unit of mol, \(n\) has unit of \(^{\circ}C\)).

Answer:

The second option: \(P = 1.2\) atm, \(V=x\) (unknown), \(n = 3.2\) mol, \(T = 293K\)