[ss10libero]

A balloon contains 0.140 g of helium at a pressure of 1.00 atm. At what temperature will the balloon have a diameter of 12.8 centimeters. Assume the balloon takes the shape of a sphere. Give your answer in degrees celcius.

volume of a sphere = 4πr3/3

Enter a numerical answer only.

[Matias Ekstrand]

Have you made an attempt on solving the problem, or have any thoughts about it?

[ss10libero]

Honestly, I have no idea where to start. I haven't learned about this topic yet, and this question is due tomorrow.

[Matias Ekstrand]

To get you started, check out the ideal gas law, and think about how it is connected to the diameter of the balloon.

[billnotgatez]

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.

[Borek]

348.5 cm^3

You forgot to multiply by pi.

[billnotgatez]

Thank you
Here is the result corrected
Let us hope I replaced all the errors
Does anyone have a different answer - significant digits ??

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
3292.52864/3
Dividing
1097.5095466666666666666666666667
Rounding
1097.5 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=1097.5 cm^3
n=0.0350 mol
R=82.05746 cm^3 atm K−1 mol−1
Therefore
T=382.13640608840265276133507979826 K
Rounded
T=382.14 K
The problems asked for temperature in C
I will use 0 C = 273.15 K
T=382.14 - 273.15
Or
T=+108.99 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.

[Borek]

Close, I got volume of 1.098 L (perhaps by using better pi than 3.14 ) and something like 109.37 deg C.

[billnotgatez]

Maybe we can call it
109 C
 

[billnotgatez]

I went to one of those on line calculators for ideal gas law

i entered the not rounded numbers and got this

Ideal Gas Law Results
Pressure 1 atm
Volume 1097.5095466666666666666666666667 cm^3
Moles 0.0349772473
Temperature 109.260027049779 C

They did not say what the R was

[billnotgatez]

I used one of those volume of sphere calculators and got
1098.066219443596

had i done that first off to check my work - i might not have all the slight errors

grrrr