Problem 68 - General Chemistry: Principles and Modern Applications

Question

Nickel can be determined as nickel dimethylglyoximate, a brilliant scarlet precipitate that has the composition \(20.31 \% \mathrm{Ni}, 33.26 \% \mathrm{C}, 4.88 \% \mathrm{H}, 22.15 \% \mathrm{O},\) and \(19.39 \%\) N. \(\mathrm{A} 15.020 \mathrm{g}\) steel sample is dissolved in concentrated HCl(aq). The solution obtained is suitably treated to remove interfering ions, to establish the proper \(\mathrm{pH},\) and to obtain a final solution volume of \(250.0 \mathrm{mL} .\) A \(10.00 \mathrm{mL}\) sample of this solution is then treated with dimethylglyoxime. The mass of purified, dry nickel dimethylglyoximate obtained is \(0.104 \mathrm{g}\) (a) What is the empirical formula of nickel dimethylglyoximate? (b) What is the mass percent nickel in the steel sample?

Step-by-Step Solution

Answer

For part (a), the empirical formula of nickel dimethylglyoximate is \( NiC_{2}H_{2}O_{2}N_{2} \). For part (b), the mass percent of nickel in the steel is approximately 10.4%.

Step 1: Finding the empirical formula

In 100g sample of nickel dimethylglyoximate, compute the amount of each element in grams using the given percentages. Also calculate the molar amounts for each element, given their atomic masses( Ni: 58.69 g/mol, C: 12.01 g/mol, H: 1.01 g/mol, O: 16.00 g/mol and N: 14.01 g/mol). For example, the molar amount of nickel = 20.31g / 58.69 g/mol = 0.346 mol.

Step 2: Determine the ratio between the numbers of moles

To work out the empirical formula, divide each molar amount by the smallest one among them. The ratios are around 1:1:1:1:1, hence the empirical formula is \( NiC_{2}H_{2}O_{2}N_{2} \).

Step 3: Calculate the quantity of nickel in steel sample

Knowing the formula, you can calculate the molar mass of nickel dimethylglyoximate as the sum of each constituent element's molar mass multiplied by the number of atoms in one molecule of it. It rounds to 288.89 g/mol.

Step 4: Mass percent of nickel in steel

Now, by dividing the molar mass of nickel by the molar mass of nickel dimethylglyoximate and multiplying by 100%, the result is the mass percent of nickel in nickel dimethylglyoximate. Then by using the mass of this compound and the volume of the solution we can find the total amount of nickel. Lastly we can find the mass percent of nickel in the steel sample by dividing the total mass of nickel by the mass of the steel sample and multiplying by 100%.

Key Concepts

Empirical Formula

Empirical formulas are a way to represent the simplest whole-number ratio of atoms in a compound. They tell us the relative number of each type of atom in the compound. For nickel dimethylglyoximate, the task is to determine this simplest ratio. You begin by assessing the given percentages of each element in a 100g sample:

• 20.31% Nickel (Ni)
• 33.26% Carbon (C)
• 4.88% Hydrogen (H)
• 22.15% Oxygen (O)
• 19.39% Nitrogen (N)

To calculate the number of moles of each element, divide the mass in grams by the respective atomic masses. After finding the moles, identify the smallest molar amount and divide all amounts by this number to obtain the simplest ratio. This process leads to finding the empirical formula, which is often different from the molecular formula but represents the foundational ratio. For nickel dimethylglyoximate, it turns out to be \( NiC_{2}H_{2}O_{2}N_{2} \).

Mass Percent Calculation

Mass percent is essentially the percentage of a particular element's mass relative to the total mass of a compound. It is a key concept for understanding the composition of a compound. To calculate the mass percent of nickel in nickel dimethylglyoximate:

• First, calculate its molar mass by adding the product of the atomic masses of each element multiplied by their respective counts in the empirical formula.
• The molar mass of nickel dimethylglyoximate calculates to approximately 288.89 g/mol.
• The mass percent of nickel itself is found by dividing the mass of nickel in the formula (58.69 g/mol) by this molar mass and then multiplying by 100%.
• This yields the mass percent of nickel within the compound's total mass.

In the exercise, this mass percent allows further calculations regarding the nickel content in the steel sample, crucial for many analytical processes.

Nickel Dimethylglyoximate

Nickel dimethylglyoximate is an important complex often used in analytical chemistry as a reagent to determine the presence of nickel in a sample due to its distinct red color when formed. In this exercise, its formation signals the presence of nickel, used within quantitative analyses. For practical usage:

• Once nickel is extracted from a sample — after removing any interfering ions, adjusting the pH, etc. — it reacts with dimethylglyoxime in the sample.
• The resulting precipitate can be weighed, providing a quantitative assessment of nickel concentration.
• Given nickel dimethylglyoximate's known composition, this reaction is a reliable indicator for nickel content.

Understanding its formula and calculating its nickel content helps in evaluating the nickel's proportion out of the mixture, as in the given problem where only 0.104 g of the complex was measured.

Analytical Chemistry

Analytical chemistry focuses on the qualitative and quantitative determination of chemicals within a sample. In the context of the Nickel dimethylglyoximate exercise, it explores methods to measure nickel in steel, a fundamental aspect of metallurgy and quality control. In practice:

• Sample preparation involves dissolving the steel in an acid, such as HCl, to separate nickel from the matrix and other additives or elements.
• The process must remove unwanted ions and maintain a controlled pH for accurate nickel assessment.
• After proper preparation, a fractional sample is treated to autonomously isolate nickel via a precipitation reaction with dimethylglyoxime.
• This is weighed for exact quantification.
• Using principles of stoichiometry and combustion analysis, one can back-calculate the total nickel present.

This highlights the discipline's critical role in providing precise measurements critical in research, industry, and compliance with various regulations.