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The addition of dimethylglyoxime, \(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2} \mathrm{~N}_{2}\), to a solution containing nickel(II) ion gives rise to a precipitate: $$ \mathrm{Ni}^{2+}+2 \mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2} \mathrm{~N}_{2} \rightarrow 2 \mathrm{H}^{+}+\mathrm{Ni}\left(\mathrm{HC}_{4} \mathrm{H}_{6} \mathrm{O}_{2} \mathrm{~N}_{2}\right)_{2} $$ Nickel dimethylglyoxime is a bulky precipitate that is inconvenient to manipulate in amounts greater than \(175 \mathrm{mg}\). The amount of nickel in a type of permanent-magnet alloy ranges between \(24 \%\) and \(35 \%\). Calculate the sample size that should not be exceeded when analyzing these alloys for nickel.

Step by step solution

01

Determine the Formulas Required

We need to find a relationship between the moles of nickel and the mass of the nickel dimethylglyoxime precipitate. The chemical equation shows that 1 mole of nickel ions reacts with 2 moles of dimethylglyoxime to form the precipitate.

02

Calculate the Molar Mass of Nickel Dimethylglyoxime

Calculate the molar mass of Ni(HC鈧凥鈧哋鈧侼鈧�)鈧�. - Molar mass of Ni: 58.69 g/mol - Molar mass of C鈧凥鈧哋鈧侼鈧�: 114.1 g/mol (calculated as 4*12.01 + 6*1.01 + 2*16.00 + 2*14.01) - Molar mass of Ni(HC鈧凥鈧哋鈧侼鈧�)鈧� = 58.69 + 2*114.1 = 286.89 g/mol

03

Calculate the Maximum Moles of Precipitate Allowed

The problem states that the maximum amount of precipitate should not exceed 175 mg, which is 0.175 g. Using the molar mass of the precipitate from Step 2, calculate the moles:\[ \text{Moles of Ni(HC鈧凥鈧哋鈧侼鈧�)鈧倉 = \frac{0.175 \text{ g}}{286.89 \text{ g/mol}} \approx 0.00061 \text{ moles} \]

04

Relate Moles of Precipitate to Moles of Nickel

From the chemical equation, 1 mole of Ni虏鈦� produces 1 mole of Ni(HC鈧凥鈧哋鈧侼鈧�)鈧� precipitate. Thus, you need 0.00061 moles of Ni虏鈦�.

05

Calculate the Mass of Nickel Required

Find the mass of nickel needed for 0.00061 moles:\[ \text{Mass of Ni} = 0.00061 \text{ moles} \times 58.69 \text{ g/mol} = 0.0358 \text{ g} \]

06

Determine Sample Size Based on Nickel Content

The alloy contains 24% to 35% nickel by weight. Find the maximum sample size using 24% as the lower bound:\[ \text{Sample size} = \frac{0.0358 \text{ g}}{0.24} \approx 0.149 \text{ g} \] And the minimum using 35% as the upper bound:\[ \text{Sample size} = \frac{0.0358 \text{ g}}{0.35} \approx 0.102 \text{ g} \]

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Key Concepts

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

Precipitation Reactions

Precipitation reactions are chemical reactions that result in the formation of an insoluble solid, known as a precipitate, when two solutions are mixed. In the context of our exercise, when dimethylglyoxime is added to a solution containing nickel(II) ions, a solid nickel dimethylglyoxime precipitate forms. Such reactions are important in analytical chemistry for isolating and removing specific ions or compounds.

• The reaction: When nickel ions (\( \text{Ni}^{2+} \)) from a solution react with dimethylglyoxime, they form a solid nickel dimethylglyoxime complex, making it easier to quantify nickel in a sample.
• In practical use: Precipitation helps chemists separate and identify components in a sample, especially when the precipitate is distinct or easily filterable.
• Characteristics: The reaction is specific because it only occurs under certain conditions and with particular compounds that can react to form a solid.

By understanding these reactions, chemists can often determine concentrations of reactive species in a solution, making it a powerful tool in both qualitative and quantitative analysis.

Molar Mass Calculation

Calculating molar mass is a critical step in chemical stoichiometry and helps in converting between grams and moles of a substance. The molar mass is obtained by summing up the atomic masses of all atoms in a molecule.
Consider the exercise's main compound, nickel dimethylglyoxime, Ni(HC鈧凥鈧哋鈧侼鈧�)鈧�.

• First, calculate the individual parts: The molar mass of Ni is 58.69 g/mol.
• For dimethylglyoxime, calculate as follows: 4 carbon atoms (4*12.01 g/mol), 6 hydrogen atoms (6*1.01 g/mol), 2 oxygen atoms (2*16.00 g/mol), and 2 nitrogen atoms (2*14.01 g/mol). This sums to 114.1 g/mol for C鈧凥鈧哋鈧侼鈧�.
• The compound molar mass: Using the above, the total molar mass of the precipitate is calculated as 58.69 + 2*114.1 = 286.89 g/mol.

Understanding molar mass allows you to convert a mass measurement into moles, helping bridge laboratory measurements and theoretical calculations.

Sample Size Determination

Sample size determination is pivotal in ensuring accurate and feasible experimental procedures, especially when dealing with specific reaction constraints. In this exercise, the concern is avoiding a precipitate volume that's too large to work with practically.

• The maximum allowable mass of nickel dimethylglyoxime precipitate is capped at 175 mg (0.175 g).
• Calculation: Using the molar mass from the previous section, you find the maximum moles of the precipitate to maintain this mass by using \( \frac{0.175 \text{ g}}{286.89 \text{ g/mol}} \approx 0.00061 \text{ moles} \).
  
• The next step involves relating these mole values to nickel content. For any given reaction, ensure the sample size doesn鈥檛 exceed these parameters to avoid inadvertently producing more precipitate than can be practically handled or measured.
• Application: For different nickel content ranges (24% to 35%), ensure maximum sample sizes are adhered to - calculated as: \( \frac{0.0358 \text{ g}}{0.24} \approx 0.149 \text{ g} \) to \( \frac{0.0358 \text{ g}}{0.35} \approx 0.102 \text{ g} \).

A well-determined sample size avoids waste and ensures accurate measurement within the lab.

Chemical Stoichiometry

Chemical stoichiometry is the calculation of reactants and products in chemical reactions, providing a quantitative relationship. In simple terms, it allows one to predict how much product will form from a given amount of reactants or vice versa.

• Given Reaction: Starting with nickel ions and dimethylglyoxime, stoichiometry helps relate moles of nickel to the precipitate formed, showing a 1:1 mole ratio.
• Mass-to-mole converts: Taking the maximum amount of precipitate (0.175 g), divide by molar mass to find moles, then back into the mass of nickel needed.
• Practical Use: In our calculation, we derived 0.00061 moles of precipitate, translating to the same moles of nickel, then calculated the mass of nickel (\(0.0358 \text{ g} \)).
• Application in Analysis: Using stoichiometric principles, you can ensure experimental setups are designed to react optimally, producing measurable, desired chemical amounts, with no excess reactant left over.

By grasping stoichiometry, students can predict and measure outcomes in the laboratory, reinforcing the theoretical predictions with empirical data.