Video: Calculating the Amount of Zinc Used in an Experiment Where a Given Mass of Zinc Is Consumed

An experiment is performed to determine the amount of hydrogen gas released in a reaction. Hydrogen gas is released by reacting hydrochloric acid with zinc metal according to the given equation. Zn(s) + 2HCl(aq) ⟶ ZnCl₂(aq) + H₂(g) All the zinc metal was consumed, and hydrogen gas was collected by displacement of water in an inverted bottle. The following data is obtained. What is the amount of zinc used, in moles? [A] 2.0 × 10⁻³ mol [B] 9.8 × 10⁻³ mol [C] 2.3 × 10⁻² mol [D] 3.0 × 10⁻² mol [E] 4.3 × 10⁻¹ mol

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Video Transcript

An experiment is performed to determine the amount of hydrogen gas released in a reaction. Hydrogen gas is released by reacting hydrochloric acid with zinc metal according to the given equation. Zn solid plus 2HCl aqueous react to form ZnCl₂ aqueous plus H₂ gas. All the zinc metal was consumed, and hydrogen gas was collected by displacement of water in an inverted bottle. The following data is obtained. What is the amount of zinc used, in moles? A) 2.0 times 10 to the minus three mole. B) 9.8 times 10 to the minus three mole. C) 2.3 times 10 to the minus two mole. D) 3.0 times 10 to the minus two mole. Or E) 4.3 times 10 to the minus one mole.

In the experiment that’s described in this question, zinc metal and hydrochloric acid or HCl are reacted. And then the gas that’s produced as a result of this reaction, hydrogen gas, is collected in a different container over water. In this part of the question, we’re simply tasked with finding the amount of zinc that’s used in moles. The mass of zinc that was used in the experiment is the first entry in the data table. It’s 0.13 grams. In the problem, we’re told that all of the zinc metal was consumed. So to find the amount of zinc that was used in the experiment, we simply have to convert the mass of zinc that was used to the amount of zinc used in moles.

The amount of a substance in moles is equal to its mass divided by the molar mass, which we can find using the periodic table. The mass of zinc given in the problem is 0.13 grams. And the molar mass of zinc is 65 grams per mole. This math looks quite tricky to do in our heads. But 65 is divisible by 13, which gives us five. In other words, 13 divided by 65 will be equal to one-fifth. All of our answer choices are expressed in the scientific notation. So we want to be able to convert this fraction to a decimal. If you don’t know what one-fifth is, express just a decimal off the top of your head. We could multiply both the top and bottom of this fraction by two to give us two-tenths.

Two-tenths expresses the decimal is 0.2. So 13 divided by 65 is 0.2. But we want to know what 0.13 divided by 65 is. Well, we can get from 13 to 0.13 by either dividing by 100 or moving the decimal place to the left twice. So we should be able to do the same thing to our answer to make everything equal, which will give us 0.002 moles. All of our answer choices are expressed in scientific notation. So our last step is converting to scientific notation. This gives us 2.0 times 10 to the minus three mole, which matches answer choice A. So the amount of zinc used in moles is 2.0 times 10 to the minus three.

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