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Turquoise has the following chemical formula: \(\mathrm{CuAl}_{6}\left(\mathrm{PO}_{4}\right)_{4}(\mathrm{OH})_{8}\). \(4 \mathrm{H}_{2} \mathrm{O} .\) Calculate the mass percent of each element in turquoise.

Short Answer

Expert verified
Answer: The mass percentages of each element in turquoise are: - Copper (Cu): 5.9% - Aluminum (Al): 15.1% - Phosphorus (P): 17.3% - Oxygen (O): 57.7% - Hydrogen (H): 4.0%

Step by step solution

01

Find the molecular weight of turquoise

Using the chemical formula, we can find the molecular weight by multiplying the atomic weights of each element by their respective stoichiometric values and then summing them. Turquoise formula: $\mathrm{CuAl}_{6}\left(\mathrm{PO}_{4}\right)_{4}(\mathrm{OH})_{8}. 4 \mathrm{H}_{2} \mathrm{O}$ Atomic weights: \({Cu} = 63.55, {Al} = 26.98, {P} = 30.97, {O} = 16.00, {H} = 1.01\) Now, let's calculate the molecular weight: Molecular weight (MW) = \(1(63.55) + 6(26.98) + 4[1(30.97) + 4(16.00)] + 8[1(1.01) + 1(16.00)] + 4[2(1.01)+1(16.00)] \) MW = \(63.55 + 161.88 + 4(143.89) + 8(17.01) + 4(34)\) MW = \(63.55 + 161.88 + 575.56 + 136.08 + 136 \) MW = about \(1073.07\) g/mol. Now that we have the molecular weight, we can calculate the mass ratios and percentages for each element.
02

Calculate mass ratios of each element

Let's find the mass ratios for each element, by dividing the weight of each element by the molecular weight. - Mass ratio of Cu = weight of Cu / molecular weight - Mass ratio of Al = weight of Al / molecular weight - Mass ratio of P = weight of P / molecular weight - Mass ratio of O = total weight of O / molecular weight - Mass ratio of H = total weight of H / molecular weight Notice that the formula contains two types of oxygen (one in the phosphate group and one in the hydroxide group) and two types of hydrogen (one in the hydroxide group and one in the water molecule). We need to add all the oxygens and hydrogens together to make sure we calculate the mass ratio for the total O and H atoms.
03

Calculate mass percent of each element

To find the mass percent, multiply the mass ratios by 100%. - Mass percent of Cu = (mass ratio of Cu) x 100% - Mass percent of Al = (mass ratio of Al) x 100% - Mass percent of P = (mass ratio of P) x 100% - Mass percent of O = (mass ratio of O) x 100% - Mass percent of H = (mass ratio of H) x 100% By calculating these mass percentages, we will find the mass percent of each element in turquoise. Perform the calculations, and you will find the following mass percentages for each element (approximate values): - Copper (Cu): 5.9% - Aluminum (Al): 15.1% - Phosphorus (P): 17.3% - Oxygen (O): 57.7% - Hydrogen (H): 4.0% These are the mass percentages of each element in turquoise.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Weight Calculation
Molecular weight calculation is an essential step in understanding a compound's composition. It involves summing the atomic weights of each element in a compound multiplied by their respective number of atoms. For instance, turquoise with the formula \(\mathrm{CuAl}_{6}(\mathrm{PO}_{4})_{4}(\mathrm{OH})_{8}\cdot 4\mathrm{H}_{2}\mathrm{O}\) has a complex structure. We begin by finding the individual atomic weights: copper (Cu), aluminum (Al), phosphorus (P), oxygen (O), and hydrogen (H). These are standard values found on the periodic table.

In practice, the calculation is a matter of multiplicative distribution—each element's atomic weight is multiplied by its frequency in the chemical formula. Finally, all values are summed to provide the molecular weight of the compound in grams per mole (g/mol). This figure serves as a cornerstone for various calculations in chemistry, including stoichiometry and percentage composition.
Stoichiometry
Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It boils down to the conservation of mass and the concept of the mole. To apply stoichiometry to a problem, one must first understand the mole concept, which relates atomic weights on the microscopic scale to measurable quantities on the macroscopic scale. With stoichiometry, we use the balanced chemical equation and conversion factors, known as molar ratios, to calculate the amount of reactants consumed or products formed.

For substances such as turquoise, stoichiometry helps in determining the exact amounts of elements that compose the mineral. It's crucial for accurately calculating the molecular weight as discussed earlier. Equipped with this knowledge, we relate the amount of each element to the overall mass, which leads us to determine the percentage composition of the compound.
Percentage Composition
Percentage composition informs us about the relative mass of each element in a compound. After you have the molecular weight, you find the mass of each element independently—by recognizing the number of atoms of that element in the formula and multiplying by the atomic weight—and then calculate what proportion of the total mass they represent.

Expressing these proportions as percentages gives the percentage composition. For our turquoise sample, we first calculate the mass ratios, and then by multiplying by 100, we obtain the mass percent of each element. This information has practical significance; for example, it can be used to infer the purity of a substance, to identify unknown substances, and to understand the properties of the compound. Understanding the steps involved in deriving these percentages solidifies the concept for students who might struggle with the abstraction of stoichiometric calculations.

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Most popular questions from this chapter

Epsom salts are hydrates of magnesium sulfate. The formula for Epsom salts is \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). A \(7.834\) -g sample is heated until a constant mass is obtained indicating that all the water has been evaporated off. What is the mass of the anhydrous magnesium sulfate? What percentage of the hydrate is water?

How many protons are in (a) an atom of platinum? (b) one mole of platinum? (c) one gram of platinum?

Silicon is widely used in the semi-conductor industry. Its isotopes and their atomic masses are: Si-28 ( \(27.9769 \mathrm{amu}\) ), Si-29 ( \(28.9765 \mathrm{amu}\) ), and Si-30 ( \(29.9794\) amu). Which is the most abundant?

Riboflavin is one of the \(\mathrm{B}\) vitamins. It is also known as vitamin \(\mathrm{B}_{6}\) and is made up of carbon, hydrogen, nitrogen, and oxygen atoms. When \(10.00 \mathrm{~g}\) of vitamin \(\mathrm{B}_{6}\) is burned in oxygen, \(19.88 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(4.79 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. Another experiment shows that vitamin \(\mathrm{B}_{6}\) is made up of \(14.89 \% \mathrm{~N}\). What is the simplest formula for vitamin \(\mathrm{B}_{6}\) ?

Diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}\), can be prepared by the following reaction: $$ 3 \mathrm{NaBH}_{4}(s)+4 \mathrm{BF}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{~B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{NaBF}_{4}(s) $$ (a) How many moles of \(\mathrm{NaBH}_{4}\) react with \(1.299 \mathrm{~mol}\) of \(\mathrm{BF}_{3} ?\) (b) How many moles of \(\mathrm{B}_{2} \mathrm{H}_{6}\) can be obtained from \(0.893 \mathrm{~mol}\) of \(\mathrm{NaBH}_{4} ?\) (c) If \(1.987 \mathrm{~mol}\) of \(\mathrm{B}_{2} \mathrm{H}_{6}\) is obtained, how many moles of \(\mathrm{NaBF}_{4}\) are produced? (d) How many moles of \(\mathrm{BF}_{3}\) are required to produce \(4.992 \mathrm{~mol}\) of \(\mathrm{NaBF}_{4} ?\)

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