Grams Of Magnesium Hydroxide Calculation A Step By Step Guide

#H1

Are you grappling with stoichiometry and need to convert formula units to grams? This comprehensive guide will walk you through the process step by step, focusing on the specific example of calculating the mass of magnesium hydroxide ($Mg(OH)_2$) in a given number of formula units. We'll break down the concepts, calculations, and reasoning behind each step, ensuring you understand not just the "how" but also the "why." This article is designed to enhance your understanding of chemical calculations and improve your problem-solving skills in chemistry. Let’s embark on this journey to understand magnesium hydroxide calculations.

Understanding the Problem: Converting Formula Units to Grams #H2

The core of this problem lies in converting between different units of measurement in chemistry. We are given the number of formula units, which is a count of individual $Mg(OH)_2$ units, and asked to find the mass in grams. This conversion requires two key steps:

1. Converting formula units to moles: Moles are the chemist’s fundamental unit for quantifying amounts of substances. One mole is defined as $6.022 imes 10^{23}$ entities (atoms, molecules, ions, or formula units), a number known as Avogadro's number. This conversion allows us to bridge the gap between the microscopic world of individual units and the macroscopic world of grams that we can measure in a lab. Think of it like converting from dozens of eggs to a measurable weight of eggs – you need a standard conversion factor.

2. Converting moles to grams: The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). The molar mass is numerically equivalent to the substance’s formula weight, which is the sum of the atomic weights of all the atoms in the chemical formula. This step allows us to directly relate the amount of substance in moles to its mass in grams, making it a crucial step in many chemical calculations. Consider it as knowing the weight of a single egg and then calculating the weight of a dozen eggs – you need the individual weight to get the total weight.

To solve this problem effectively, it’s essential to grasp these concepts and their interrelationships. Understanding these conversions is fundamental not only for this specific problem but also for a wide array of chemical calculations. These steps involve fundamental principles of stoichiometry, the quantitative relationship between reactants and products in chemical reactions.

Step-by-Step Solution: Calculating Grams of $Mg(OH)_2$ #H2

Now, let’s apply these concepts to the specific problem of calculating the grams of $Mg(OH)_2$ in $7.5 imes 10^{23}$ formula units. We'll break down the solution into manageable steps, explaining the reasoning behind each step and highlighting the relevant conversion factors. Understanding each step will empower you to tackle similar problems with confidence.

Step 1: Convert Formula Units to Moles #H3

To convert formula units to moles, we use Avogadro's number as the conversion factor. We know that 1 mole of any substance contains $6.022 imes 10^{23}$ formula units. This relationship allows us to set up a conversion factor where Avogadro's number is in the denominator, ensuring that the formula units cancel out, leaving us with moles. The formula for this conversion is:

Moles = (Number of Formula Units) / (Avogadro's Number)

In our case, we have $7.5 imes 10^{23}$ formula units of $Mg(OH)_2$. Plugging this value into the equation:

Moles of $Mg(OH)_2$ = $(7.5 imes 10^{23} ext{ f.un.}) / (6.022 imes 10^{23} ext{ f.un./mol})$

Calculating this gives us approximately 1.245 moles of $Mg(OH)_2$. This conversion is crucial because moles provide a standardized unit to relate the number of particles to the mass of the substance. This step is analogous to converting a count of items to a standardized unit like dozens before converting to weight.

Step 2: Convert Moles to Grams #H3

To convert moles to grams, we use the molar mass of $Mg(OH)_2$. The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). To calculate the molar mass of $Mg(OH)_2$, we sum the atomic masses of each element in the formula, which are obtained from the periodic table:

• Magnesium (Mg): 24.31 g/mol
• Oxygen (O): 16.00 g/mol (x2 because there are two oxygen atoms)
• Hydrogen (H): 1.01 g/mol (x2 because there are two hydrogen atoms)

Therefore, the molar mass of $Mg(OH)_2$ is:

Molar Mass of $Mg(OH)_2$ = 24.31 g/mol + 2(16.00 g/mol) + 2(1.01 g/mol) = 58.33 g/mol

Now, we can use the molar mass as a conversion factor to convert moles of $Mg(OH)_2$ to grams. The formula for this conversion is:

Grams = (Moles) × (Molar Mass)

Using the 1.245 moles we calculated in Step 1:

Grams of $Mg(OH)_2$ = (1.245 mol) × (58.33 g/mol) ≈ 72.5 g

So, there are approximately 72.5 grams of $Mg(OH)_2$ in $7.5 imes 10^{23}$ formula units. This final conversion gives us the answer in a unit that is directly measurable in the lab, highlighting the practical significance of these calculations. This step completes the bridge from the microscopic world of formula units to the macroscopic world of grams.

Identifying the Conversion Factor #H2

The problem also asks which part of the conversion factor goes in the