Question

The active ingredient in milk of magnesia (an antacid) is magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2}\). A typical dose (one (a) the tablespoon) contains \(1.2 \mathrm{~g}\) of \(\mathrm{Mg}(\mathrm{OH})_{2} .\) Calculate molar mass of magnesium hydroxide and (b) the amount of magnesium hydroxide (in moles) in one tablespoon.

Short answer

Molar mass of Mg(OH)_2 is 58.33 g/mol; there are approximately 0.0206 moles in 1.2 g.

Step-by-step solution

Calculate the Molar Mass of Magnesium Hydroxide

To find the molar mass of magnesium hydroxide, \( \mathrm{Mg(OH)_2} \), we need to sum the atomic masses of its constituent elements. The atomic mass of magnesium \( \mathrm{Mg} \) is approximately \( 24.31 \) g/mol, oxygen \( \mathrm{O} \) is \( 16.00 \) g/mol, and hydrogen \( \mathrm{H} \) is \( 1.01 \) g/mol.Given the formula \( \mathrm{Mg(OH)_2} \), we have 1 magnesium, 2 oxygens, and 2 hydrogens:\[\text{Molar Mass} = 1(24.31) + 2(16.00) + 2(1.01) = 24.31 + 32.00 + 2.02 = 58.33\, \text{g/mol}\]

Calculate Moles of Magnesium Hydroxide

To determine the number of moles of magnesium hydroxide in 1.2 g, use the formula:\[\text{Moles} = \frac{\text{mass in grams}}{\text{molar mass}}\]Substituting the given values:\[\text{Moles} = \frac{1.2}{58.33} \approx 0.0206 \text{ moles}\]

Key concepts

Molar Mass Calculation

Calculating the molar mass is a fundamental skill in chemistry that helps us determine how many grams one mole of a substance weighs. To calculate the molar mass of a compound like magnesium hydroxide, we first need to break down the compound into its individual elements and understand their atomic masses.
For magnesium hydroxide, the chemical formula is \(\mathrm{Mg(OH)_2}\). This means:

• 1 atom of magnesium \((\mathrm{Mg})\), with an atomic mass of approximately 24.31 g/mol,
• 2 atoms of oxygen \((\mathrm{O})\), each with an atomic mass of 16.00 g/mol,
• 2 atoms of hydrogen \((\mathrm{H})\), each with an atomic mass of 1.01 g/mol.

To find the total molar mass, we sum these contributions:\[1(24.31) + 2(16.00) + 2(1.01) = 58.33\, \text{g/mol}\]
This tells us that one mole of magnesium hydroxide weighs 58.33 grams. Understanding molar mass helps in converting between grams and moles, a critical step in many chemical calculations.

Magnesium Hydroxide

Magnesium hydroxide \(\mathrm{Mg(OH)_2}\) is commonly used as an antacid, often found in a product called 'milk of magnesia'. It helps to neutralize stomach acid, providing relief from indigestion and heartburn.
This compound is composed of magnesium, oxygen, and hydrogen. Knowing its chemical structure is essential for understanding how it interacts in reactions and its role in medicine. The magnesium ion

• (\(\mathrm{Mg^{2+}}\)) provides the basic properties,
• while the hydroxide ions \((\mathrm{OH^-})\) can combine with hydrogen ions \((\mathrm{H^+})\)

to form water, reducing acidity.
Magnesium hydroxide is not just a simple antacid; it has important roles in both laboratory and industrial processes due to its ability to precipitate as a solid and because of its alkaline nature. Each function in these scenarios involves understanding its chemical behavior at a molecular level.

Chemical Formulas

Chemical formulas are a shorthand way of representing a substance's composition. They tell us which elements are included in a compound and in what ratio they are present. This is extremely helpful for predicting the way compounds behave in chemical reactions.
A compound like magnesium hydroxide is written as \(\mathrm{Mg(OH)_2}\), which tells us:

• There is one magnesium atom per unit of the compound.
• Two hydroxide groups per unit, each consisting of one oxygen and one hydrogen atom.

Chemical formulas allow chemists to quickly understand the structure of a compound and provide a foundation for calculating molar masses, balancing equations, and predicting the outcomes of reactions.
Understanding chemical formulas is key to success in chemistry because they are the language in which chemists express chemical ideas and reactions. They articulate not only what molecules are present but also the specific arrangements and numbers of atoms within a compound, giving clarity to complex chemical interactions.