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

Video transcript

Hello everyone. Today, we have the following problem if sulfur dioxide molecules are placed at 450 degrees. Kelvin, what is the most probable speed of the molecules at this temperature? A 3.4 times 10 to the second mo meters per second. B 1.2 times 10 to the second meters per second. C 1.2 times 10 to the fifth meters per second or D 1.9 times 10 to the fifth meters per second. So the first step is to identify the molar mass of the sulfur dioxide. And that can be done by looking at the periodic table and identifying the molar mass of one sulfur atom, which is approximately 32.066 g per mole. And then we can add that to the molar mass of one oxygen molecule or one oxygen atom which is 16.00 g per mole. But then we have to multiply that 16 by two since there are two oxygen molecules and this gives us a molar mass of 64.0 66 g per mole. Now, we can put the values that we were given and that we have now into the speed of gas molecules equation which states that the most probable speed is equal to the square root of two multiplied by a gas constant. R multiplied by the temperature in degrees Kelvin divided by the molar mass. So we have the square root in the numerator, we have two multiplied by a gas constant, which can be found in reference text is 8.314 joules per mole. Kelvin multiplying that by the temperature which we have is 450 degrees Kelvin and then dividing that by the molar mass, which is this molar mass should actually be converted to kilograms. And so we can multiply by the conversion factor that 10 to the third grams equals 1 kg. And when we do that, we get rid of units of grams and we arrive at 0.064066 kg per mole. So we will input this into our molar mass. Now because we have jewels in the numerator, we have to get rid of that unit. We can use the conversion factor that joules can actually represent or be represented by kilograms multiplied by meters squared, divided by a second squared. So this can actually be rewritten as 8.314 kilograms multiplied by meters squared, divided by second squared multiplied by moles multiplied by the temperature. And Kelvin solving for the most probable speed of gas, we get an answer of 341.75. However, if we can, if we convert this using significant figures and two, to be exact, we would get 3.4 times 10 to the second meters per squared. And if we look at our answer choices, ancho a best reflects this value. And with that, we have solved the problem overall, I hope it helped. And until next time.