8. na₂o₂ + h₂(so₄) na(so₄) + h₂o₂

9. n₂ + h₂ nh₃

10. al +o₂ al₂o₃

11. kmno₄ k₂o + mno + o₂

Answers:

8. Na₂O₂ + H₂(SO₄) → Na₂(SO₄) + H₂O₂

9. N₂ + 3 H₂ → 2 NH₃

10. 4 Al + 3 O₂ → 2 Al₂O₃

11. 4 KMnO₄ → 2 K₂O + 4 MnO + 5 O₂

Step by step solution:

8. Na₂O₂ + H₂(SO₄) → Na₂(SO₄) + H₂O₂

In this chemical equation we have:

On the left side:          On the right side:

Na: 2 atoms                 Na: 2 atoms

O: 2+4=6 atoms           O: 4+2=6 atoms

H: 2 atoms                    H: 2 atoms

S: 1 atom                        S: 1 atom

We have the same quantity of atoms on both sides of the equation, then the equation is balanced.

9. N₂ + H₂ → NH₃

In this chemical equation we have:

On the left side:          On the right side:

Na: 2 atoms                 Na: 1 atom

H: 2 atoms                   H: 3 atoms

The equation is not balanced.

We need to multiply the molecule of NH₃ on the right side of the equation by 2 to get 2 Na atoms on the right side:

N₂ + H₂ → 2 NH₃

Now, we have 2(3)=6 H atoms on the right side of the equation, then we must multiply the molecule of H₂ on the left side by 3 to get 3(2)=6 H atoms on the left side of the equation:

N₂ + 3 H₂ → 2 NH₃

10. Al + O₂ → Al₂O₃

In this chemical equation we have:

On the left side:          On the right side:

Al: 1 atom                     Al: 2 atoms

O: 2 atoms                   O: 3 atoms

The equation is not balanced.

The least common multiple between the quantity of atoms of O of the left side (2) and the right side (3) is 2*3=6, then let's multiply the molecule of O₂ on the left side by 3 and the molecule of  Al₂O₃ on the right side by 2 to get 6 O atoms on both side of the equation:

Al + 3 O₂ → 2 Al₂O₃

Now we have 2(2)=4 Al atoms on the right side of the equation and only 1 Al atom on the left side, then let's multiply the Al atom on the left side by 4:

4 Al + 3 O₂ → 2 Al₂O₃

11. KMnO₄ → K₂O + MnO + O₂

In this chemical equation we have:

On the left side:          On the right side:

K: 1 atom                      K: 2 atoms

Mn: 1 atom                   Mn: 1 atom

O: 4 atoms                   O: 1+1+2=4 atoms

The equation is not balanced

If we suppose that the coefficients are:

a KMnO₄ → b K₂O + c MnO + d O₂

We have on the left side "a" Mn atoms and on the right side "c" Mn atoms, and they must be equal then a=c:

a KMnO₄ → b K₂O + a MnO + d O₂

We have "a" K atoms on the left side and b(2)=2b K atoms on the right side, then a=2b

And we have on the left side a(4)=4a O atoms and on the right side

b+a+d(2)=b+a+2d O atoms, and they must be equal, then:

4a=b+a+2d

and a=2b, replacing in the equation above:

4(2b)=b+2b+2d

8b=b+2b+2d

Adding like terms on the left side of the equation:

8b=3b+2d

Solving for d: Subtracting 3b from both sides of the equation:

8b-3b=3b+2d-3b

5b=2d

Dividing both sides of the equation by 2:

5b/2=2d/2

5b/2=d

d=5b/2

Then b must be an even number to get a whole number for d, using the least even number for b=2

d=5(2)/2→d=5

and a=2b=2(2)→a=4

Then the equation balanced is:

4 KMnO₄ → 2 K₂O + 4 MnO + 5 O₂

Now we have:

On the left side:          On the right side:

K: 4 atoms                   K: 2(2)=4 atoms

Mn: 4 atoms                Mn: 4 atoms

O: 4(4)=16 atoms         O: 2+4+5(2)=2+4+10=16 atoms

The equation is balanced

area of focus

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle