HCl (g)
Hbr(g)
HF(g)
Which of these gases has the fastest average speed? The highest average kinetic energy?
How do I determine this?
To determine which of these gases has the fastest average speed, you can use Graham's law of effusion. According to Graham's law, the rate of effusion (or the speed) of a gas is inversely proportional to the square root of its molar mass.
1. Calculate the molar mass of each gas:
- HCl (g): 1 hydrogen atom (1.007 g/mol) + 1 chlorine atom (35.45 g/mol) = 36.46 g/mol
- HBr(g): 1 hydrogen atom (1.007 g/mol) + 1 bromine atom (79.90 g/mol) = 80.91 g/mol
- HF(g): 1 hydrogen atom (1.007 g/mol) + 1 fluorine atom (18.998 g/mol) = 20.00 g/mol
2. Take the square root of each molar mass:
- HCl (g): √36.46 g/mol ≈ 6.04 g/mol
- HBr(g): √80.91 g/mol ≈ 8.99 g/mol
- HF(g): √20.00 g/mol ≈ 4.47 g/mol
From these calculations, we can see that HBr has the highest molar mass and, therefore, the slowest average speed. On the other hand, HF has the lowest molar mass and the fastest average speed.
To determine which gas has the highest average kinetic energy, you can use the equation for kinetic energy (KE). The average kinetic energy of a gas is directly proportional to its temperature.
Since the temperature is not provided, we cannot determine the gas with the highest average kinetic energy without that information. Temperature affects the kinetic energy, so the gas with the highest temperature would have the highest average kinetic energy.