What is the temperature?

Question

what is the temperature of the gas inside a 750mL balloon filled with.300 grams of H2 gas? The pressure of the balloon is 1.2 atm

Answer 1

Summary of the problem:

V = 750mL convert to Liter to be 0.75L

(750mL* 1L/1000mL = 0.75L)

m of H₂ gas = 0.3g

p = 1.2 atm

R = 0.082057 (L *atm)/ (mol*K)

T = ? Kevin

Solve:

Finding the mole of H₂ gas:

Mole = mass/(Molar Mass) = 0.3g/(1.008g*2) = 0.1488 mol

Using the “Ideal Gas Law” formular pV = nRT:

T = (pV/nR) = [(1.2atm)*(0.75L)]/[(0.1488 mol)*(0.082057) (L *atm)/(mol*K)] = 73.7 K

73.7 K ~~ 74. K (2 significant figures)

Temperature is 7.4 Kevin at this condition.

Answer 2

This is an ideal gas law problem and you will use the following equation to calculate the temperature (T).

You will use the ideal gas law equation: pV = nRT.

p = pressure (in units of atmospheres (atm))

V = volume (in units of liters (L))

n = moles of the substance (mol) (it's a number that is dependent on the molecular weight of a substance)

R = gas constant = 0.0821 L-atm/mol-K

T= temperature in Kelvin (K)

To solve for temperature, you rearrange the equation (pV = nRT) above to get temperature by itself.

So, divide both sides by nR to solve for T. So T = pV/nR

Next convert your values, because they have to be in the right units:

Volume: 750 mL = 0.75 L (because there is 1000 mL in 1 L)

To convert grams to moles, you divide the mass (0.3) by the molecular weigh of H2 (2) =

0.3/2 = 0.15 mol

Nothing needs to be done for pressure, since it's given in atm (the proper unit) and we already know what R is.

Now plug in your variables to solve for T = pV/nR

1. p = 1.2 atm
2. V= 0.75L
3. n = 0.15 mol
4. R = 0.0821 L-atm/mol-K

Using the values above, we calculate the T = pV/nR

T = 1.2 atm (0.75L)/(0.15 mol) (0.0821 L-atm/mol-K)

T = 0.9 atm-L / 0.12315 L-atm/K)

T = 73.11 K

To check, just plug all the respective numbers back into the original ideal gas law equation and one side MUST be equal to the other. If it doesn't then, you know the answer is wrong :-)

pV = nRT

1.2 (0.75) = 0.15 (0.0821) (73.1)

0.9 = 0.9

This confirms your temperature value is correct! Good luck and hope this was helpful!

Dr. M.