a. The total translational kinetic energy of the gas molecules is 1672 Joules.
b. The thermal energy of a gas molecule is equal to 1672 Joules.
c. The rms speed of the gas molecules is equal to 512.83 m/s.
Given the following data:
Scientific data:
a. To calculate the total translational kinetic energy of the gas molecules:
First of all, we would determine the number of moles of hydrogen gas contained in 1.3 grams:
Note: Molar mass of hydrogen gas = 2 g/mol.
[tex]Number \;of \;moles = \frac {mass}{molar\;mass}\\\\Number \;of \;moles = \frac {1.3}{2}[/tex]
Number of moles = 0.65 moles.
Next, we would determine the number of molecules in 0.65 moles of hydrogen gas:
By stoichiometry:
1 mole = [tex]6.02 \times 10^{23}[/tex] molecules.
0.65 mole = X molecules.
Cross-multiplying, we have:
X = [tex]0.65 \times 6.02 \times 10^{23}[/tex] = [tex]3.913 \times 10^{23}[/tex] molecules.
Mathematically, total translational kinetic energy is given by this formula:
[tex]T = \frac{1}{2} mc^2[/tex]
Substituting the given parameters into the formula, we have;
[tex]T = \frac{1}{2} \times 2 \times 1.67 \times 10^{-27} \times 3.913 \times 10^{23} \times (1600)^2\\\\T = 6.53 \times 10^{-4} \times 2560000[/tex]
T = 1,671.68 ≈ 1672 Joules.
b. In Science, the total translational kinetic energy is equal to the thermal energy of a gas molecule.
Thermal energy = 1672 Joules.
c. To calculate the rms speed of the gas molecules:
[tex]Net\;energy = 500 + 1672 -2000[/tex]
Net energy = 172 Joules.
For the rms speed:
[tex]172 = \frac{1}{2} \times 2 \times 1.67 \times 10^{-27} \times 3.913 \times 10^{23} \times c^2\\\\172 = 6.54 \times 10^{-4} c^2\\\\c = \sqrt{\frac{172}{6.54 \times 10^{-4}} } \\\\c=\sqrt{262996.95}[/tex]
c = 512.83 m/s.
Read more on rms speed here: https://brainly.com/question/7427089
