Problem 129 - General Chemistry

Question

Zinc acetate is sometimes prescribed by physicians for the treatment of Wilson's disease, which is a genetically caused condition wherein copper accumulates to toxic levels in the body. If you were to analyze a sample of zinc acetate and find that it contains \(3.33 \times 10^{23}\) acetate ions, how many grams of zinc acetate must be present in the sample?

Step-by-Step Solution

Answer

The sample contains approximately 50.75 grams of zinc acetate.

Step 1: Determine Moles of Acetate Ions

To find the number of moles of acetate ions in the sample, divide the number of acetate ions by Avogadro's number, which is approximately \(6.022 \times 10^{23}\) ions/mol. \[ \text{Moles of acetate ions} = \frac{3.33 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.553 \text{ moles} \]

Step 2: Relate Moles of Acetate Ions to Moles of Zinc Acetate

Each formula unit of zinc acetate has two acetate ions. Thus, the moles of zinc acetate is half the moles of acetate ions. \[ \text{Moles of zinc acetate} = \frac{0.553}{2} \approx 0.2765 \text{ moles} \]

Step 3: Calculate Grams of Zinc Acetate

Find the molar mass of zinc acetate \((\text{Zn(C}_2\text{H}_3\text{O}_2\text{)}_2)\). The molar mass is computed as follows:- Zinc (Zn): \(65.38\text{ g/mol}\)- Carbon (C): \(12.01\text{ g/mol} \times 4 = 48.04\text{ g/mol}\)- Hydrogen (H): \(1.01\text{ g/mol} \times 6 = 6.06\text{ g/mol}\)- Oxygen (O): \(16.00\text{ g/mol} \times 4 = 64.00\text{ g/mol}\)Adding these, the molar mass of zinc acetate is \(183.50\text{ g/mol}\).Now, calculate the mass of zinc acetate by multiplying the moles by the molar mass.\[ \text{Mass of zinc acetate} = 0.2765 \text{ moles} \times 183.50 \text{ g/mol} \approx 50.75 \text{ grams} \]

Key Concepts

Zinc Acetate

Zinc acetate is an inorganic compound commonly used in dietary supplements and some over-the-counter medications. It's particularly interesting for its role in treating Wilson's disease, a condition that leads to copper accumulation in the body. In chemistry, zinc acetate is known for forming a dihydrate compound, which means each molecule of zinc acetate comes with two water molecules. Its chemical formula is often written as Zn(C\(_2\)H\(_3\)O\(_2\))\(_2\)·2H\(_2\)O. This helps it stabilize and explains its white crystalline appearance. Understanding zinc acetate's structure is crucial, especially when performing calculations involving moles and mass. Each molecule consists of zinc atoms bound to acetate ions, and these ions are key players when determining the amount of substance present. So, if you're tackling problems on zinc acetate, remember that it is more than just an average salt, playing a vital role in biological and chemical processes.

Chemical Formula

When dealing with chemical compounds, the chemical formula offers a clear representation of what elements are present and in what proportion. Let's take zinc acetate's formula: Zn(C\(_2\)H\(_3\)O\(_2\))\(_2\). This compounds' formula tells us that each molecule consists of one zinc atom (Zn), two acetate ions (C\(_2\)H\(_3\)O\(_2\)), where each acetate ion is made up of two carbon, three hydrogen, and two oxygen atoms.Knowing how to read and understand a chemical formula is critical for calculating molar masses and determining the roles of various ions within a compound. Importantly, for zinc acetate, keep in mind its specific composition also involves water of crystallization, known as hydrate molecules, which can impact calculations related to mass and concentration. Understanding this will help demystify a lot of chemistry problems.

Avogadro's Number

Avogadro's number is a cornerstone in chemistry, vital in connecting the macroscopic world we can see to the microscopic world of atoms and molecules. Named after the scientist Amedeo Avogadro, this number is defined precisely as 6.022 × 10\(^{23}\) entities per mole. Whether you're dealing with atoms, ions, or molecules, using Avogadro's number allows you to convert between amounts in moles and countable numbers of particles. In practice, when you're given a number of acetate ions, for instance, Avogadro's number can help you figure out how many moles of those ions you have in your sample. This conversion is foundational in achieving accurate chemical calculations and gaining deeper insights into how substances behave at the molecular level.

Moles to Grams Conversion

The process of converting moles to grams is a fundamental skill in chemistry that links the theoretical world of equations to practical measurements. To convert moles to grams, you must multiply the number of moles by the molar mass of the substance. This is because the molar mass, found on the periodic table—a sum of atomic masses of elements in a compound—tells you how much one mole of the substance weighs in grams. For example, with zinc acetate, once you've determined the number of moles you have, simply multiply by its molar mass—183.50 g/mol in this case—to find out the total mass in grams. Practically speaking, this allows chemists to prepare solutions with exact concentrations and understand proportions in reactions. It's essential to learn this conversion process to smoothly bridge understanding between abstract concepts and real-world applications.