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Nickel(II) sulfide, NiS, occurs naturally as the relatively rare mineral millerite. One of its occurrences is in meteorites. To analyze a mineral sample for the quantity of NiS, the sample is dissolved in nitric acid to form a solution of \(\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}\) $$\begin{aligned} \mathrm{NiS}(\mathrm{s})+& 4 \mathrm{HNO}_{3}(\mathrm{aq}) \rightarrow \\ & \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{NO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{S}(\mathrm{s}) \end{aligned}$$ The aqueous solution of \(\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}\) is then reacted with the organic compound dimethylglyoxime \(\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{N}_{2} \mathrm{O}_{2}\right)\) to give the red solid \(\mathrm{Ni}\left(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{N}_{2} \mathrm{O}_{2}\right)_{2}\). Suppose a \(0.468-\mathrm{g}\) sample containing millerite produces \(0.206 \mathrm{g}\) of red, solid \(\mathrm{Ni}\left(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{N}_{2} \mathrm{O}_{2}\right)_{2}\) What is the mass percent of NiS in the sample?

Step by step solution

01

Calculate Molar Mass of Ni(C4H7N2O2)2

First, calculate the molar mass of the red solid, \( \mathrm{Ni}\left(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{N}_{2} \mathrm{O}_{2}\right)_{2} \). The formula consists of 1 Ni, 8 C, 14 H, 4 N, and 4 O. - \( \text{Ni} : 58.69 \ g/mol \) - \( \text{C} : 12.01 \times 8 = 96.08 \ g/mol \) - \( \text{H} : 1.01 \times 14 = 14.14 \ g/mol \) - \( \text{N} : 14.01 \times 4 = 56.04 \ g/mol \) - \( \text{O} : 16.00 \times 4 = 64.00 \ g/mol \)Add these together to get:\[ \text{Molar mass of } \mathrm{Ni(C_4H_7N_2O_2)_2} = 58.69 + 96.08 + 14.14 + 56.04 + 64.00 = 288.95\ g/mol \]

02

Determine Moles of Red Solid Produced

Calculate the moles of \( \mathrm{Ni(C_4H_7N_2O_2)_2} \) produced using its molar mass:\[ \text{Moles} = \frac{0.206\ g}{288.95\ g/mol} \approx 0.000713\ mol \]

03

Calculate Moles of NiS in Sample

The stoichiometry of the reaction producing the solid indicates a 1:1 molar ratio between \( \mathrm{Ni(C_4H_7N_2O_2)_2} \) and \( \mathrm{NiS} \). So, the moles of \( \mathrm{NiS} \) are the same:\[ 0.000713\ mol \]

04

Calculate Mass of NiS

Find the molar mass of \( \mathrm{NiS} \):- \( \text{Ni} : 58.69 \ g/mol \) - \( \text{S} : 32.07 \ g/mol \)\[ \text{Molar mass of } \mathrm{NiS} = 58.69 + 32.07 = 90.76\ g/mol \]Now, calculate the mass of \( \mathrm{NiS} \):\[ \text{Mass} = 0.000713\ mol \times 90.76\ g/mol \approx 0.0647\ g \]

05

Calculate Mass Percent of NiS

The mass percent of \( \mathrm{NiS} \) in the sample is:\[ \text{Mass percent of } \mathrm{NiS} = \left( \frac{0.0647\ g}{0.468\ g} \right) \times 100\% \approx 13.83\% \]

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Key Concepts

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

Nickel(II) sulfide

Nickel(II) sulfide, commonly represented as \(\text{NiS}\), is an inorganic compound consisting of nickel and sulfur atoms. This compound is naturally found as the mineral millerite. In chemistry exercises involving Nickel(II) sulfide, it is important to understand its distinct properties and reactions. NiS is notably found in meteorites and is often studied for its applications in analysis and synthesis.

To identify the quantity of NiS in a sample, the compound is often dissolved in a strong oxidizing agent, such as nitric acid (\(\text{HNO}_3\)). During this process, a chemical reaction occurs in which the compound is broken down and transformed into nickel nitrate (\(\text{Ni(NO}_3\text{)}_2\)), among other products. Analyzing Nickel(II) sulfide is crucial in various fields, including mineralogy and materials science, where precise quantification and purity assessment are needed.

Molar mass calculation

Molar mass calculation is a fundamental concept in stoichiometry, allowing us to determine the mass of one mole of a chemical compound. For complex structures, such as \(\mathrm{Ni(C_4H_7N_2O_2)_2}\), each element's atomic mass is multiplied by the number of times it appears in the formula, and then these values are summed up to find the total molar mass.

Here’s how this process is broken down:

• First, identify the individual molar masses for each type of atom in the compound, such as nickel (\(\text{Ni} = 58.69\ g/mol\)), carbon (\(\text{C} = 12.01\ g/mol\)), hydrogen (\(\text{H} = 1.01\ g/mol\)), nitrogen (\(\text{N} = 14.01\ g/mol\)), and oxygen (\(\text{O} = 16.00\ g/mol\)).
• Multiply each element's molar mass by the number of atoms of that element in a molecule of the compound.
• Add all these values together to get the total molar mass of the compound.

Calculating the molar mass is essential for converting mass quantities to moles, which can then be used in further stoichiometric calculations in reaction analysis.

Chemical reaction analysis

Chemical reaction analysis involves understanding and predicting the yield and proportions of products formed in a reaction from given reactants. For the reaction involving NiS and \(\text{HNO}_3\), we observe the transformation of reactants into various products, one important one being nickel nitrate (\(\text{Ni(NO}_3\text{)}_2\)), along with gases and water.

Analyzing such reactions requires:

• Identifying the reactants and products involved in the reaction.
• Using balanced chemical equations to understand the mole-to-mole relationships between reactants and products.
• Applying the stoichiometry principles to relate the amounts of reactants to the quantities of products.

In this case, a 1:1 molar ratio exists between produced \(\text{Ni(C}_4\text{H}_7\text{N}_2\text{O}_2\text{)}_2\) and initial \(\text{NiS}\), which means that the number of moles of \(\text{NiS}\) is identical to the moles of the nickel-dimethylglyoxime complex produced. Understanding the stoichiometry in these reactions is crucial for accurate chemical analysis and calculation of mass percentages in compounds.