krishnachaurasia7060
Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Consider the following chemical equation:
[tex]\[a \, Al_2O_3 + b \, HCl \longrightarrow c \, AlCl_3 + d \, H_2O\][/tex]

In order to balance this chemical equation, the values of [tex]\(a, b, c\)[/tex], and [tex]\(d\)[/tex] must be:

A. [tex]\(1, 6, 2,\)[/tex] and [tex]\(3\)[/tex]

B. [tex]\(1, 6, 3,\)[/tex] and [tex]\(2\)[/tex]

C. [tex]\(2, 6, 2,\)[/tex] and [tex]\(3\)[/tex]

D. [tex]\(2, 6, 3,\)[/tex] and [tex]\(2\)[/tex]

Sagot :

GinnyAnswer
To balance the chemical equation:
[tex]\[ a \, \mathrm{Al_2O_3} + b \, \mathrm{HCl} \longrightarrow c \, \mathrm{AlCl_3} + d \, \mathrm{H_2O} \][/tex]

we must determine the correct coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] such that the number of atoms for each element is equal on both sides of the equation.

Starting with the unbalanced equation:

[tex]\[ \mathrm{Al_2O_3} + \mathrm{HCl} \longrightarrow \mathrm{AlCl_3} + \mathrm{H_2O} \][/tex]

Let's follow a step-by-step process to balance it:

### 1. Balance Aluminum (Al):
On the left side, we have 2 Al atoms in [tex]\(\mathrm{Al_2O_3}\)[/tex], so we need the same number of Al atoms on the right side. Since [tex]\(\mathrm{AlCl_3}\)[/tex] contains 1 Al atom, we need 2 moles of [tex]\(\mathrm{AlCl_3}\)[/tex]:

[tex]\[ a \, \mathrm{Al_2O_3} + b \, \mathrm{HCl} \longrightarrow 2 \, \mathrm{AlCl_3} + d \, \mathrm{H_2O} \][/tex]

### 2. Balance Chlorine (Cl):
Now, we have 2 moles of [tex]\(\mathrm{AlCl_3}\)[/tex], and each mole of [tex]\(\mathrm{AlCl_3}\)[/tex] contains 3 Cl atoms, giving us a total of [tex]\(2 \times 3 = 6\)[/tex] Cl atoms on the right side. Thus, to balance the Cl atoms, we need 6 moles of HCl on the left side:

[tex]\[ a \, \mathrm{Al_2O_3} + 6 \, \mathrm{HCl} \longrightarrow 2 \, \mathrm{AlCl_3} + d \, \mathrm{H_2O} \][/tex]

### 3. Balance Hydrogen (H):
Each mole of HCl contains 1 H atom, giving us 6 H atoms on the left side. On the right side, each mole of [tex]\(\mathrm{H_2O}\)[/tex] contains 2 H atoms. Therefore, we need 3 moles of [tex]\(\mathrm{H_2O}\)[/tex] to balance the 6 H atoms:

[tex]\[ a \, \mathrm{Al_2O_3} + 6 \, \mathrm{HCl} \longrightarrow 2 \, \mathrm{AlCl_3} + 3 \, \mathrm{H_2O} \][/tex]

### 4. Balance Oxygen (O):
Finally, we need to balance the O atoms. On the left side, we have 3 O atoms in [tex]\(\mathrm{Al_2O_3}\)[/tex]. On the right side, we have 3 O atoms in [tex]\(3 \, \mathrm{H_2O}\)[/tex]. This matches, so the O atoms are balanced:

[tex]\[ \mathrm{Al_2O_3} + 6 \, \mathrm{HCl} \longrightarrow 2 \, \mathrm{AlCl_3} + 3 \, \mathrm{H_2O} \][/tex]

Thus, the balanced equation is:
[tex]\[ \mathrm{Al_2O_3} + 6 \, \mathrm{HCl} \longrightarrow 2 \mathrm{AlCl_3} + 3 \mathrm{H_2O} \][/tex]

Therefore, the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] are:
[tex]\[ (a, b, c, d) = (1, 6, 2, 3) \][/tex]

This matches with option (A).

So, the correct answer is:
(A) [tex]\(1, 6, 2, 3\)[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.