Na + H20 -> NaOH+ H2 ( balance the equation in algebric method
The Correct Answer and Explanation is:
Balanced Chemical Equation (Using Algebraic Method):
Unbalanced equation:
Na + H₂O → NaOH + H₂
Step-by-Step Algebraic Balancing Method
We assign algebraic variables to each compound:
Let:
- aaa = number of Na atoms
- bbb = number of H₂O molecules
- ccc = number of NaOH molecules
- ddd = number of H₂ molecules
So the equation becomes:
aNa+bH2O→cNaOH+dH2a \text{Na} + b \text{H}_2\text{O} \rightarrow c \text{NaOH} + d \text{H}_2aNa+bH2O→cNaOH+dH2
Now write equations based on atom conservation:
1. Sodium (Na):
Each Na atom appears once on both sides:
a=ca = ca=c
2. Hydrogen (H):
Left side: Each H₂O has 2 H atoms → total H atoms = 2b
Right side:
- Each NaOH has 1 H → contributes ccc
- Each H₂ molecule has 2 H atoms → contributes 2d2d2d
So:
2b=c+2d2b = c + 2d2b=c+2d
3. Oxygen (O):
Each H₂O has 1 O → total O = b
Each NaOH has 1 O → total O = c
So:
b=cb = cb=c
Now solve the system of equations:
From equation 1:
a=ca = ca=c
From equation 3:
b=cb = cb=c
So, substitute a=b=ca = b = ca=b=c into equation 2:
2b=b+2d2b = b + 2d2b=b+2d
Solve for ddd:
2b−b=2d2b – b = 2d2b−b=2d
b=2db = 2db=2d
⇒ d=b2d = \frac{b}{2}d=2b
Since the smallest whole number solution requires no fractions, let’s choose b=2b = 2b=2:
Then:
a=b=c=2a = b = c = 2a=b=c=2,
d=22=1d = \frac{2}{2} = 1d=22=1
Balanced Equation:
2Na + 2H₂O → 2NaOH + H₂
Explanation (Like in Textbooks):
The reaction between sodium metal (Na) and water (H₂O) produces sodium hydroxide (NaOH) and hydrogen gas (H₂). To ensure the law of conservation of mass is upheld, the equation must be balanced so that the number of atoms for each element is the same on both sides.
Using algebraic variables, each substance is assigned a coefficient. Equations are formed by matching the total number of atoms of each element on both sides. Solving the system shows that two sodium atoms react with two water molecules to produce two sodium hydroxide molecules and one hydrogen molecule. This maintains the correct ratio of sodium, hydrogen, and oxygen atoms.
The final balanced chemical equation is:
2Na + 2H₂O → 2NaOH + H₂.
