Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Balance the following reaction with the smallest possible integer coefficients. What is the coefficient of lithium sulfite? For blank coefficients, assign a value of 1.

[tex]? BF_3 + Li_2SO_3 \longrightarrow ? B_2(SO_3)_3 + ? LiF[/tex]

Sagot :

GinnyAnswer
To balance the chemical equation involving the reaction of boron trifluoride ([tex]\(BF_3\)[/tex]) and lithium sulfite ([tex]\(Li_2SO_3\)[/tex]), we need to ensure that the number of each type of atom on the reactant side is equal to the number on the product side.

Given unbalanced reaction:
[tex]\[ ?\, BF_3 + Li_2SO_3 \longrightarrow ?\, B_2(SO_3)_3 + ?\, LiF \][/tex]

Let's proceed step-by-step:

### Step 1: Determine the Atoms Involved
- Boron (B)
- Fluorine (F)
- Lithium (Li)
- Sulfur (S)
- Oxygen (O)

### Step 2: Set up the Unbalanced Equation with Coefficients
Assume the coefficients are [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] for [tex]\(BF_3\)[/tex], [tex]\(Li_2SO_3\)[/tex], [tex]\(B_2(SO_3)_3\)[/tex], and [tex]\(LiF\)[/tex] respectively:
[tex]\[ a\, BF_3 + b\, Li_2SO_3 \longrightarrow c\, B_2(SO_3)_3 + d\, LiF \][/tex]

### Step 3: Balance Each Element
1. Boron (B):
Each [tex]\(BF_3\)[/tex] has 1 Boron, and each [tex]\(B_2(SO_3)_3\)[/tex] has 2 Borons:
[tex]\[ a = 2c \][/tex]

2. Fluorine (F):
Each [tex]\(BF_3\)[/tex] has 3 Fluorines, and each [tex]\(LiF\)[/tex] has 1 Fluorine:
[tex]\[ 3a = d \][/tex]

3. Lithium (Li):
Each [tex]\(Li_2SO_3\)[/tex] has 2 Lithiums, and each [tex]\(LiF\)[/tex] has 1 Lithium:
[tex]\[ 2b = d \][/tex]

4. Sulfur (S):
Each [tex]\(Li_2SO_3\)[/tex] has 1 Sulfur, and each [tex]\(B_2(SO_3)_3\)[/tex] has 3 Sulfurs:
[tex]\[ b = 3c \][/tex]

5. Oxygen (O):
Each [tex]\(Li_2SO_3\)[/tex] has 3 Oxygens, and each [tex]\(B_2(SO_3)_3\)[/tex] has 9 Oxygens:
(This is inherently balanced if [tex]\(b\)[/tex] and [tex]\(c\)[/tex] are balanced as determined from sulfur)

### Step 4: Solve the System of Equations
From our constraints, we can express all coefficients in terms of [tex]\(c\)[/tex]:
1. Boron: [tex]\(a = 2c\)[/tex]
2. Fluorine: [tex]\(3a = d\)[/tex] => [tex]\(3(2c) = d\)[/tex] => [tex]\(d = 6c\)[/tex]
3. Lithium: [tex]\(2b = d\)[/tex] => [tex]\(2b = 6c\)[/tex] => [tex]\(b = 3c\)[/tex]

### Step 5: Determine the Smallest Integer Coefficients
Let [tex]\(c = 1\)[/tex]:
1. [tex]\(a = 2c = 2(1) = 2\)[/tex]
2. [tex]\(b = 3c = 3(1) = 3\)[/tex]
3. [tex]\(d = 6c = 6(1) = 6\)[/tex]

### Step 6: Write the Balanced Equation
[tex]\[ 2\, BF_3 + 3\, Li_2SO_3 \longrightarrow 1\, B_2(SO_3)_3 + 6\, LiF \][/tex]

Therefore, the coefficient of lithium sulfite ([tex]\(Li_2SO_3\)[/tex]) is [tex]\(\boxed{3}\)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.