(c) Calculate the most probable speeds of Cl₂ molecules at 300 K.

Video transcript

Hello, everyone. Today, we have the following problem. A certain amount of roaming gas is placed inside a container at 550 degrees. Kelvin determine the most probable speed of the molecules at this temperature. And choices A 3d are all in meters per second with a being 7.6 B being 9.3 C being 2.4 times 10 to the second. And D being 2.9 times 10 to the second. So we can use the equation to solve for this multiple speed using the multiple speed is equal to the square root of two multiplied by Arbi as a gas constant multiplied by temperature in degrees Kelvin divided by the molar mass. Now, we can find the molar mass of this bromine gas by referring to the periodic table and taking the mass of one bromine atom which is 79.9 g per mole. And multiplying that by two, since we have two atoms of this brome, and that will give us or, and when we actually have that we will need to convert to kilograms for our equation. So we will use the conversion factor and multiply by 1 kg is equal to 10 to the to the third grams, getting rid of units of grams and giving us an ultimate molar mass of 0.1598 kilograms per mole. Now, with our equation, if we rewrite it or if we were to move it over to the right, we would have the most probable speed is equal to the square root of two multiplied by gas constant, which will be 8.314. And usually it'd be in terms of joules per moles times Kelvin. However, there is a conversion factor that joules or units of jewels is equal to kilograms multiplied by meters squared, divided by seconds squared. And this will come into play with our molar mass. So we have 8.3 1 4 kg multiplied by meters squared that will be divided by seconds squared. And then the rest of the gas constant, which is moles times Kelvin, that value will be multiplied by the degrees which is or by the temperature which is 550 degrees Kelvin. And then all of that still under the square root will be divided by the molar mass which is 0.1598 kg per mole. And our units of moles will cancel out as will units of kilograms and temperature such that we get a most probable speed that is equal to 239.2285 m per second. And if we were to convert this or refer to this in terms of significant figures. We would use two significant figures such that we have 2.4 times 10 to the second meters per squared as our answer. And if we go to Andros, Andros c best reflects it value overall, I hope this helped. And until next time.