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In chemistry, the concept of moles helps us understand how much of a substance we have. To find the number of moles of a solid compound like NaOH, we use its mass and molar mass, which is the mass of one mole of that substance.
First, we find the molar mass of NaOH. Sodium hydroxide (NaOH) has a molar mass of about 40 g/mol. This means each mole of NaOH weighs 40 grams. When you have 1.75 grams of NaOH, you can convert this to moles by dividing the mass by the molar mass.
The calculation is: \[ ext{Moles of NaOH} = \frac{1.75 ext{ g}}{40 ext{ g/mol}} = 0.04375 ext{ mol} \]This shows you that in this exercise, we are starting with 0.04375 moles of NaOH. This foundational knowledge is essential for proceeding with any calculations involving chemical reactions.

In a chemical reaction, the limiting reagent is the reactant that is completely consumed first, stopping the reaction from proceeding. Identifying the limiting reagent involves comparing the mole ratios of the reactants according to the balanced chemical equation.
In the reaction between NaOH and NiCl\( _2 \) \[ ext{NiCl}_2 + 2 ext{NaOH} \rightarrow ext{Ni(OH)}_2 \downarrow + 2 ext{NaCl} \]we see that it takes 2 moles of NaOH to fully react with 1 mole of NiCl\(_2 \).
Given we have 0.025 moles of NiCl\(_2 \) and 0.04375 moles of NaOH, we need 0.050 moles of NaOH to completely react with the NiCl\(_2 \).
However, since we only have 0.04375 moles of NaOH, NaOH is the limiting reagent. It limits how far the reaction can go because we will run out of NaOH before we use all the NiCl\(_2 \). Understanding which reagent is limiting helps us determine the maximum amount of product that can be formed.

The reaction equation represents how reactants transform into products. It provides a clear picture of what happens chemically. For this problem, the equation \[ ext{NiCl}_2 + 2 ext{NaOH} \rightarrow ext{Ni(OH)}_2 \downarrow + 2 ext{NaCl} \]illustrates the interaction between nickel chloride and sodium hydroxide.
The equation tells us that for every mole of nickel chloride (NiCl\(_2 \)) that reacts, two moles of sodium hydroxide (NaOH) are consumed, producing one mole of nickel hydroxide (Ni(OH)\(_2 \)) and two moles of sodium chloride (NaCl).
The arrow indicates the direction of the reaction, showing that the compounds on the left (reactants) turn into those on the right (products). The downward arrow next to Ni(OH)\(_2 \) signifies that it is a precipitate, meaning it forms a solid in the mixture which can separate out of the solution. Using the equation helps in predicting the amount of product formed and knowing the reactants' relationships.

The solubility product constant, denoted as \( K_ ext{sp} \),is an essential concept for understanding how compounds dissolve - or don't dissolve - in water. It specifically applies to sparingly soluble salts, like nickel hydroxide, Ni(OH)\(_2 \).A lower \( K_ ext{sp} \) value indicates lower solubility in water.For Ni(OH)\(_2 \) the provided\( K_ ext{sp} \) of1.6 × 10\(^{-14} \) tells us that it is not very soluble, giving us insight into how much of it will dissolve in our solution.The mathematical expression for \( K_ ext{sp} \)is \[[ ext{Ni}^{2+}] [ ext{OH}^-]^2 = K_ ext{sp}\]where [ ext{Ni}^{2+}]is the concentration of nickel ions, and [ ext{OH}^-]^2the square of the hydroxide ions concentration.This equilibrium expression is pivotal when predicting if a precipitate will form in a reaction.By comparing calculated ionic product values to the given \( K_ ext{sp} \) we can determine if the solution will have excess ions beyond what the precipitate can dissolve, leading to precipitation.