What is the minimum amount of 6.0 M H 2 SO 4 necessary to produce 25.0 g of H 2 (g) according to the reaction between aluminum and sulfuric acid? 2 Al(s) + 3 H 2 SO 4 (aq) → Al 2 (SO 4 ) 3 (aq) + 3 H 2 (g)

All right. Hi, everyone. So this question is asking us what is the minimum amount of 6.0 molar H two. So four necessary to produce 25.0 g of hydrogen gas according to the reaction between aluminum and sulfuric acid. So that's two moles of aluminum react with three moles of sulfuric acid to produce one mole of aluminum sulfate and three moles of hydrogen gas. So here we also have four different answer choices labeled A through D proposing different volumes of the sulfuric acid solution. So let's go ahead and get started. Now, in this case, we're going to have to use dimensional analysis to relate the mass of hydrogen gas produced to the amount of sulfuric acid necessary when this reaction begins. Right. So in this case, we're going to use quite a few conversion factors. So before we discuss how that works, I want to just point out that the amount of hydrogen gas or H two is provided in units of grams. And in this case, we're provided with a balanced chemical equation that relates the moles of reactants to the moles of products. So our first conversion factor would have to be the molar mass to go from grams of H two moles of H two. And so recall that the molar mass of hydrogen gas is equal to 2.016 g per month. So let's go ahead and get started with our dimensional analysis. The first value that should always be written is the information that you are given, right? So first, I'm going to start with my 25.0 g of H two. And the first thing I'm going to do is convert from grams of H two to moles of H two using the molar mass. Now, in this case, I'm going to treat conversion factors as if they were fractions with a numerator and a denominator. The idea is to always make sure that your starting units cancel out and you're left with a new set of units. In the case of this particular first step, the idea is to cancel out units of grams and convert that into moles. This means that grams should cancel out when applying my molar mass. So in this case, when applying the molar mass of H two units of moles should go in the numerator and grams should go in the denominator because this ensures that my grams of H two cancel out to yield moles. So now that I have moles of hydrogen gas, I can use the mole ratios provided in the balanced chemical equation to convert from moles of H two to moles of sulfuric acid because recall that were trying to find how much sulfuric acid is necessary to produce 25.0 g of H two. Now, according to the balanced chemical equation, right, three moles of sulfuric acid correspond with three moles of H two. So those are the exact values that I'm going to use in my next conversion factor. Now, recall that right now our units are moles of H two. This means that in my second conversion factor that uses the mole ratios, moles of H two should go in the denominator because once again, my old units have canceled out, specifically moles of H two have canceled out. And now my answer is going to be referring to the moles of sulfuric acid. So at this point, we've calculated how many moles of sulfuric acid are necessary to produce 25.0 g of hydrogen gas. So now we're going to use the molarity provided or the molar concentration of sulfuric acid to find the volume necessary for the reaction. So my molar concentration here is going to be my third and final conversion factor. In which in this case, there are 6.0 moles of H two. So four per every 1 L of solution. So when he's using my third conversion factor, my moles of sulfuric acid should go in the denominator to make sure that those units cancel out, which means that leaders should go in the numerator moles of H two. So four cancel out. And now we can go ahead and calculate our final answer which will be expressed in units of liters of H two. So four. So after multiplying all numerators and dividing by the denominators and rounding to two significant figures, our answer ends up being 2.1 L of H two. So four and this corresponds to option D in the multiple choice and there you have it. So it, if you watch this video all the way up to the end. Thank you very much for watching. I appreciate it. And I hope you found this helpful.

Ch.5 - Introduction to Solutions and Aqueous Solutions

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Tro 5th Edition

Ch.5 - Introduction to Solutions and Aqueous Solutions

Problem 32

Chapter 5, Problem 32

What is the minimum amount of 6.0 M H₂SO₄ necessary to produce 25.0 g of H₂(g) according to the reaction between aluminum and sulfuric acid? 2 Al(s) + 3 H₂SO₄(aq) → Al₂(SO₄)₃(aq) + 3 H₂(g)

Verified step by step guidance

Determine the molar mass of H_2 by adding the atomic masses of hydrogen atoms.

Calculate the moles of H_2 produced using the formula: moles = mass / molar mass.

Use the stoichiometry of the balanced chemical equation to find the moles of H_2SO_4 needed. According to the equation, 3 moles of H_2SO_4 produce 3 moles of H_2.

Calculate the volume of 6.0 M H_2SO_4 solution required using the formula: volume = moles / molarity.

Ensure the units are consistent and convert the volume to the desired unit if necessary.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the proportions of substances involved in a reaction, which is essential for converting between grams and moles. In this case, stoichiometry will help us find out how much sulfuric acid is needed to produce a specific mass of hydrogen gas.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for understanding how much of a concentrated solution, like 6.0 M H2SO4, is required to achieve a desired amount of product. By knowing the molarity, we can calculate the volume of sulfuric acid needed to react with aluminum to produce the specified amount of hydrogen gas.

Limiting Reactant

The limiting reactant is the substance that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed. Identifying the limiting reactant is essential for accurately calculating the quantities of reactants needed. In this scenario, we need to ensure that we have enough sulfuric acid to react with aluminum to produce the desired amount of hydrogen gas.