Balance the following the chemical equation:
a
1:1:2:1
b
2:1:1:1
c
1:2:1:1
d
1:1:1:2
To balance the chemical equation, we need to adjust the coefficients of the molecules so that the number of atoms on both sides is equal.
a + b2 -> c + d
The ratios of atoms in each molecule are:
a: 1 a, 1 b, 2 c, 1 d
b: 2 a, 1 b, 1 c, 1 d
c: 1 a, 2 b, 1 c, 1 d
d: 1 a, 1 b, 1 c, 2 d
To balance the equation, we can start by adjusting the atoms that appear in unequal proportions. In this case, the molecule "b" has twice as many "a" atoms as the molecule "a". To equalize the number of "a" atoms, we need to multiply molecule "a" by 2:
2a + b2 -> c + d
Now, we have:
a: 2 a, 2 b, 4 c, 2 d
b: 2 a, 1 b, 1 c, 1 d
c: 1 a, 2 b, 1 c, 1 d
d: 1 a, 1 b, 1 c, 2 d
Next, we need to equalize the number of "b" atoms. In this case, we need to multiply the molecule "b" by 2:
2a + 2b2 -> c + d
Now, we have:
a: 2 a, 2 b, 4 c, 2 d
b: 4 a, 2 b, 2 c, 2 d
c: 1 a, 2 b, 1 c, 1 d
d: 1 a, 1 b, 1 c, 2 d
At this point, the number of "a" and "b" atoms is balanced, but the number of "c" atoms on each side is unequal. To equalize the number of "c" atoms, we need to multiply the molecule "c" by 4:
2a + 2b2 -> 4c + d
Now, we have:
a: 2 a, 2 b, 4 c, 2 d
b: 4 a, 2 b, 2 c, 2 d
c: 4 a, 8 b, 4 c, 4 d
d: 1 a, 1 b, 1 c, 2 d
Finally, the number of "d" atoms on each side is unequal. To equalize the number of "d" atoms, we need to multiply the molecule "d" by 2:
2a + 2b2 -> 4c + 2d
Now, we have:
a: 2 a, 2 b, 4 c, 2 d
b: 4 a, 2 b, 2 c, 2 d
c: 4 a, 8 b, 4 c, 4 d
d: 2 a, 2 b, 2 c, 4 d
The balanced chemical equation is:
2a + 2b2 -> 4c + 2d