Question

(a) Balance the following equation, and tell how many moles of nickel will react with \(9.81 \mathrm{~mol}\) of hydrochloric acid. \(\mathrm{Ni}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NiCl}_{2}(a q)+\mathrm{H}_{2}(g)\) (b) How many moles of \(\mathrm{NiCl}_{2}\) can be formed in the reaction of \(6.00 \mathrm{~mol}\) of \(\mathrm{Ni}\) and \(12.0 \mathrm{~mol}\) of \(\mathrm{HCl} ?\)

Short answer

4.905 moles of Ni react with 9.81 moles of HCl. 6.00 moles of \(\text{NiCl}_2\) are formed.

Step-by-step solution

Balance the Chemical Equation

To balance the chemical equation \( \text{Ni}(s) + \text{HCl}(aq) \rightarrow \text{NiCl}_{2}(aq) + \text{H}_{2}(g) \), first look at each element. Ni appears once on both sides, so start with H and Cl. There are two Cl atoms in \( \text{NiCl}_2 \), so you need 2 \( \text{HCl} \) to balance it: \[ \text{Ni}(s) + 2 \text{HCl}(aq) \rightarrow \text{NiCl}_{2}(aq) + \text{H}_{2}(g) \]. Now, both Cl and H are balanced. Check Ni (1 on each side), and H (2 on each side), so the equation is balanced.

Calculate Nickel Moles for Question (a)

Using the balanced equation: 1 mole of Ni reacts with 2 moles of HCl. Thus, to find the moles of Ni that react with 9.81 moles of HCl, use the stoichiometric ratio: \( \frac{1 \text{ mole Ni}}{2 \text{ moles HCl}} \). Therefore, \( x \text{ moles Ni} = \frac{9.81 \text{ moles HCl}}{2} \). Calculate the result: \( x = 4.905 \text{ moles of Ni} \).

Determine the Limiting Reagent for Question (b)

With 6.00 mol of Ni and 12.0 mol of HCl, use the stoichiometric ratio: 1 mole of Ni requires 2 moles of HCl. Thus, 6 moles of Ni require \( 6 \times 2 = 12 \text{ moles of HCl} \). Since both reactants can fully react, neither is in excess.

Calculate Moles of \(\text{NiCl}_2\) Formed - Question (b)

From the balanced equation, 1 mole of Ni produces 1 mole of \(\text{NiCl}_2\). Since all 6.00 moles of Ni can react completely (as there are 12.0 moles of HCl available), 6.00 moles of \(\text{NiCl}_2\) will be formed, according to the stoichiometry.

Key concepts

Chemical Equation Balancing

Balancing chemical equations is crucial because it ensures that the conservation of mass is maintained. In the reaction \[ \mathrm{Ni}(s) + \mathrm{HCl}(aq) \rightarrow \mathrm{NiCl}_{2}(aq) + \mathrm{H}_{2}(g) \], we start by comparing the number of atoms of each element before and after the reaction.
The nickel (Ni) atom appears once on both sides, so nickel is initially balanced. However, the chlorine (Cl) and hydrogen (H) atoms are not balanced. On the right side, in \( \mathrm{NiCl}_{2} \), there are two chlorine atoms. This means we need two moles of \( \mathrm{HCl} \) to balance the chlorine.
Now the equation looks like this: \[ \mathrm{Ni}(s) + 2 \mathrm{HCl}(aq) \rightarrow \mathrm{NiCl}_{2}(aq) + \mathrm{H}_{2}(g) \].This gives us two H atoms on the left, which matches the two H atoms in the hydrogen gas \( \mathrm{H}_{2} \) on the right. Now, all elements are balanced.

Limiting Reagent

The concept of a limiting reagent is key in stoichiometry as it determines how much product can be formed in a reaction. In any chemical reaction, the limiting reagent is the reactant that is completely consumed first, limiting the amount of product formed.
In our exercise, we are given two reactants:

• 6.00 moles of Ni
• 12.0 moles of HCl

Using the balanced equation from before, where 1 mole of Ni reacts with 2 moles of HCl, we can see that 6 moles of Ni would require 12 moles of HCl to completely react.
In this case, both reactants are available in the exact quantities needed to fully react with each other, meaning neither is in excess, and both are used up completely. Therefore, there is no limiting reagent, and all reactant material will convert to products.

Moles Calculation

Calculating moles is an essential step in stoichiometry that helps us to quantify how much of a substance is involved in a reaction.
In our original exercise, we have two examples where moles calculations are necessary.First, determine how many moles of Ni are needed to react with a given amount of HCl. Using the balanced equation, 1 mole of Ni reacts with 2 moles of HCl. Thus, if you have 9.81 moles of HCl, you can find the moles of Ni using the ratio: \[x = \frac{9.81 \text{ moles HCl}}{2} = 4.905 \text{ moles Ni}\]In the second example, for calculating the moles of \( \mathrm{NiCl}_2 \) formed, the balanced equation tells us that 1 mole of Ni produces 1 mole of \( \mathrm{NiCl}_2 \). Given 6.00 moles of Ni, if all of it can react, you will produce 6.00 moles of \( \mathrm{NiCl}_2 \). This straightforward conversion showcases how stoichiometry and moles calculation play together to predict the outcomes in chemical reactions.