I think it has been long enough that I can attempt the solving of this problem and not doing someone's homework for them.
I may have got the significant digits wrong along the way.
Someone correct me if I made a mistake.
We could look at this problem as an Ideal Gas Law Problem.
PV=nRT
We are given the pressure, how much Helium we have and the volume can be computed.
We just have to covert them so they can be used in the equation.
Since se are asked for T
T=(PV)/(nR)
For n we need the moles.
Helium has 4.002602 grams per mole
Since we have 0.140 grams of helium
We have 0.0349772473 moles of helium
Which is about 0.0350 moles
For V we need to find the volume of the sphere
The balloon is 12.8 centimeters in diameter
Or has a radius of 6.4 centimeters
We are given the formula for the volume of a sphere
Using x for multiplication, / for division and ^ for power the formula is as follows and using 3.14 for the constant Pi
The formula for a sphere is as follows
(4 x 3.14 x radius ^ 3)/3
Substituting the radius
(4 x 3.14 x 6.4 ^ 3)/3
Doing the cube calculation first
(4 x 3.14 x 262.144)/3
Multiplying
1045.436/3
Dividing
348.47866666666666666666666666667
Rounding
348.5 cm^3
Now R is a constant and we can go to a table of ideal gas constants and select one that has the same units we have for the variables.
Or we can convert the variables to the units in an ideal gas constant that we are using.
Many times I use 0.0821 L atm K−1 mol−1
But that does not have the same units we have
I could convert the units of the variables but there is an ideal gas constant that has this problems units
82.05746 cm^3 atm K−1 mol−1
So Given
Formula
T=(PV)/(nR)
Pressure
P=1.00 atm
V=348.5 cm^3
n=0.0350 mol
R=82.05746 cm^3 atm K−1 mol−1
Therefore
T=121.34354216110097903173145814095 K
Rounded
T=121.34 K
The problems asked for temperature in C
I will use 0 C = 273.15 K
T=121.34 - 273.15
Or
T=-151.81 C
To solve this problem
I selected the proper equation for the situation
I converted units and / or calculated variables necessary for this problem
Selected the correct Ideal Gas Law Constant or change my variables to have the same units as my selected constant
Then solved the equation.