A 500 mL metal cylinder holding 0.100 moles of helium gas is known to rupture at a pressure of 10 atmospheres. At what temperature, in °C, will the container fail?
Here is what I came up with:
T= (1.00mol x 0.0821 LxATM/KxMOL) / 10atm x 0.5L
=0.01642K
Convert to C: 0.01642K - 273 = -272.98 C
That can't possibly be right. Please help.
Note that you substituted 1.00 mole for n and not 0.100 mol; also, you inverted the formula when you solved for T.
PV = nRT and rearrange to
T = PV/nR = (10)(0.500)/(0.100)(0.08206) = 609.3 K
609.3-273.15 = 336.16 which rounds to 336 C.
I was giving the answer key with the correct answer at 336 C.
Now i'm really confused... Can someone explain.
No that is correct the answer will turn out to be a negative number.
stupid responder
Well, it seems like you've got a serious case of cold feet with this problem. Let me warm things up a bit with some humor!
Now, I'm about to bring the heat and shed some light on your calculations. The formula you used is almost spot on, but there's a tiny hiccup in your math. Let's break it down together:
T = (n x R) / (P x V)
Where:
n = number of moles
R = ideal gas constant (0.0821 L x atm / K x mol)
P = pressure
V = volume
Given:
n = 0.100 moles
P = 10 atm
V = 500 mL (which we need to convert to liters, so V = 0.5 L)
Now let's crunch the numbers:
T = (0.100 mol x 0.0821 L x atm / K x mol) / (10 atm x 0.5 L)
T = 0.01642 K
But don't fret yet, my friend! We're not quite done. We need to convert Kelvin to Celsius by subtracting 273.
T = 0.01642 K - 273 °C
Now, when we put the numbers together, we get approximately -272.98358 °C. My scientific clown calculations say that this is the temperature at which your cylinder might rupture.
So, cheer up! Remember, science doesn't have to be cold and rigid. It can be full of laughs and warm smiles too!
To find the temperature at which the container will fail, you can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L∙atm/K∙mol)
T = temperature (in Kelvin)
First, we need to convert the given pressure from atmospheres to Pascals (Pa). Since 1 atm = 101,325 Pa, the pressure in Pascals would be:
10 atm x 101,325 Pa/atm = 1,013,250 Pa
To convert from Celsius to Kelvin, we use the formula: K = °C + 273.15
Now, let's rearrange the Ideal Gas Law equation to solve for T:
T = (PV) / (nR)
Substituting the given values:
T = (1,013,250 Pa) / (0.100 mol x 0.0821 L∙atm/K∙mol x 0.500 L)
T = 24,583,536.1 K
Converting this temperature to Celsius:
T = 24,583,536.1 K - 273.15 = 24,583,262.95 °C
It seems that there was an error in the calculations. The correct temperature, in °C, at which the container will fail is approximately 24,583,262.95 °C.