Upon decomposition, one sample of magnesium fluoride produces 1.65 kg of magnesium and 2.57 kg of fluorine. A second sample produces 1.32 kg of magnesium. How much fluorine (in grams) does the second sample produce?

Video transcript

Welcome back everyone. We have two samples of calcium bromide which have undergone a decomposition reaction. We're told that sample a produced 2.63 kg of calcium and 10.5 kg of bromine. If sample be produced, 3.6 kg of calcium. What is the expected mass of bromine produced in kilograms? We're going to begin by recalling that a decomposition reaction consists of our compound in this case calcium bromide solid, which decomposes into its separate elements where we have calcium solid form and then our second product is bromine gas, which exists naturally as a gaseous halogen. And so these would be the two reactions the two decomposition reactions that occur now recognize that were given information on each of our samples. We have sample A and then we have sample be described and according to the prompt sample A consists of 2.63 kg of our product Calcium produced. And this is per our mass of bromine produced for sample a as 10.5 kg. What we've written out is a representation of a mass ratio. And we can set an equation equal to the information given in the prompt for sample B, which states that our mass of calcium produced in sample B is 3.6 kg. Now we don't know our denominator, which is our mass of being produced. And so we would say we have X kilograms of bromine in our denominator. And so you can see that all we need to do now is solve for our denominator. And so to simplify, we're just going to cross multiply on both sides so that we have the following equation being 2. kg of calcium multiplied by X. And will use the color red multiplied by X kilograms of bro. Mean Which is set equal to the product of 3.6 kg of calcium Multiplied by 10.5 kg of bromine because we need to isolate for our mass of kilograms of bromine from sample to or sample be rather we want to divide both sides By 2.63 kg of calcium so that it cancels out on the left hand side and on the right hand side we would just place our numerator in brackets since that's the operation we want to handle first. And then when we finally divide by our denominator, we would be able to cancel out our units of kilograms of calcium. And so what we would simplify too. And sorry, we can actually also cancel out these units here, since we are taking the product of our numerator. And so this will simplify to our mass of romaine equal to a value Of the results of our quotient being 14.37 in which we can round to exactly 14.4 kg of bro mean that will be produced from the decomposition and sample b. And so it's highlighted in yellow represents our final answer corresponding to choice a. In the multiple choice. So I hope this was helpful and let us know if you have any questions.