Magnesium Phosphate: Calculating Reactant Mass

Hey guys! Ever wondered how much magnesium you need to react with phosphoric acid to get a specific amount of magnesium phosphate? It's a classic chemistry problem involving stoichiometry, and we're going to break it down step by step. This article will guide you through calculating the mass of magnesium required to react completely with 50.0 cm³ of 1.24 mol/dm³ phosphoric acid ($H_3PO_4$) to produce magnesium phosphate ($Mg_3(PO_4)_2$). So, grab your calculators, and let's dive in!

Understanding the Chemical Reaction

Before we jump into calculations, let's make sure we're clear on the chemistry involved. The reaction between magnesium (Mg) and phosphoric acid ($H_3PO_4$) produces magnesium phosphate ($Mg_3(PO_4)_2$) and hydrogen gas ($H_2$). The balanced chemical equation is crucial for stoichiometric calculations:

$3 Mg(s) + 2 H_3PO_4(aq) \longrightarrow Mg_3(PO_4)_2(aq) + 3 H_2(g)$

This equation tells us that 3 moles of magnesium react with 2 moles of phosphoric acid to produce 1 mole of magnesium phosphate and 3 moles of hydrogen gas. This mole ratio is the key to solving our problem. Make sure to always have a balanced equation before starting any stoichiometry calculations, or your results will be way off! So, the balanced equation here is like our recipe, telling us exactly how much of each ingredient we need.

Stoichiometry: The Heart of the Calculation

Stoichiometry is a fancy word, but all it really means is the study of the quantitative relationships between reactants and products in chemical reactions. In simpler terms, it's about figuring out how much of one thing you need to react with another. We'll use the mole ratios from the balanced equation as conversion factors. These ratios help us translate between the amount of phosphoric acid we have and the amount of magnesium we need. Stoichiometry ensures that we're using the right proportions of reactants to avoid waste and achieve the desired product yield. Think of it like baking a cake – you need the right amount of flour, sugar, and eggs to get a delicious result. If you add too much of one ingredient, the cake won't turn out right!

Importance of a Balanced Equation

As highlighted earlier, the balanced equation is the cornerstone of any stoichiometric calculation. It provides the precise mole ratios necessary for accurate computations. Without a balanced equation, we wouldn't know how many moles of each reactant are required to fully react with each other. This would lead to incorrect calculations and, consequently, an inaccurate determination of the mass of magnesium needed. The coefficients in the balanced equation represent the molar ratios, acting as conversion factors that link the quantities of different substances involved in the reaction. So, double-check your balanced equation – it's the foundation of your entire calculation!

Step-by-Step Calculation

Now, let's break down the calculation into manageable steps.

Step 1: Calculate Moles of Phosphoric Acid ($H_3PO_4$)

We're given the volume (50.0 cm³) and concentration (1.24 mol/dm³) of phosphoric acid. First, we need to convert the volume from cm³ to dm³ (since 1 dm³ = 1000 cm³):

Volume in $dm^3$ = 50.0 $cm^3$ / 1000 $cm^3$/$dm^3$ = 0.0500 $dm^3$

Next, we can calculate the number of moles of $H_3PO_4$ using the formula:

Moles = Concentration × Volume

Moles of $H_3PO_4$ = 1.24 mol/$dm^3$ × 0.0500 $dm^3$ = 0.0620 mol

So, we have 0.0620 moles of phosphoric acid. This is our starting point for figuring out how much magnesium we need. It's like knowing how many eggs you have in a recipe – it helps you determine how much of the other ingredients you need.

Understanding Molarity and Volume Conversion

The concept of molarity (mol/dm³) is crucial in these calculations. Molarity expresses the concentration of a solution, indicating the number of moles of solute per liter (or cubic decimeter) of solution. Converting the volume from cm³ to dm³ is necessary to align the units and ensure accurate calculations. Failing to perform this conversion would lead to a tenfold error in the result. Always double-check your units to avoid common mistakes. Remember, paying attention to units is like proofreading your work – it can catch errors before they become a problem!

Step 2: Determine Moles of Magnesium (Mg) Required

Using the balanced equation, we know that 3 moles of Mg react with 2 moles of $H_3PO_4$. We can use this mole ratio to find the moles of Mg needed:

Moles of Mg = Moles of $H_3PO_4$ × (3 mol Mg / 2 mol $H_3PO_4$)

Moles of Mg = 0.0620 mol $H_3PO_4$ × (3 mol Mg / 2 mol $H_3PO_4$) = 0.0930 mol Mg

So, we need 0.0930 moles of magnesium to react completely with the phosphoric acid. This step uses the mole ratio from the balanced equation, which is why having a correct balanced equation is so vital. Think of it like a recipe conversion – if you're doubling a recipe, you need to double all the ingredients proportionally.

Applying Mole Ratios from the Balanced Equation

The mole ratio derived from the balanced equation is the linchpin of this step. It allows us to convert from the known quantity of phosphoric acid to the unknown quantity of magnesium. By understanding and applying these ratios, we can accurately determine the required amount of reactants. This step demonstrates the practical application of stoichiometry in chemical calculations. It's like using a map to navigate – the mole ratio is our guide, showing us the correct path to the answer.

Step 3: Calculate Mass of Magnesium (Mg)

Finally, we can calculate the mass of magnesium using its molar mass (24.31 g/mol):

Mass = Moles × Molar Mass

Mass of Mg = 0.0930 mol × 24.31 g/mol = 2.26 g

Therefore, we need 2.26 grams of magnesium to react completely with the 50.0 cm³ of 1.24 mol/dm³ phosphoric acid. We've arrived at our final answer! This step is where we convert from moles to grams, giving us a practical amount of magnesium that we can measure out in the lab.

Converting Moles to Mass Using Molar Mass

The molar mass of a substance is the mass of one mole of that substance, usually expressed in grams per mole (g/mol). It serves as a conversion factor between the number of moles and the mass of a substance. By multiplying the number of moles of magnesium by its molar mass, we can determine the mass of magnesium required for the reaction. This step completes the calculation, providing us with the answer in a practical unit (grams). It's like translating from one language to another – molar mass is our dictionary, helping us convert between moles and grams.

Conclusion

So, guys, to prepare magnesium phosphate by reacting magnesium with 50.0 cm³ of 1.24 mol/dm³ phosphoric acid, you'll need approximately 2.26 grams of magnesium. This calculation demonstrates the power of stoichiometry and how we can use balanced chemical equations to determine the quantities of reactants needed in a chemical reaction. Understanding these concepts is crucial for anyone studying chemistry. Keep practicing, and you'll become a stoichiometry pro in no time! Remember, chemistry is like a puzzle – each piece (concept) fits together to create a complete picture. By mastering stoichiometry, you're adding another important piece to your chemical knowledge!