Question

Question regarding significant figures ..

Following this conversion, would it be correct to have only 1 significant figure for the answer, because we have multiplied with (2 mol / 5 mol) which only has 1 sig fig.

Could you confirm this calculation is correct in regards to the significant figures?

0.105 g Na₂C₂O₄ * (1 mol / 134 g Na₂C₂O₄) * (2 mol KMnO₄ / 5 mol Na₂C₂O₄) = 0.0003 --> 3x10^-4

3*10^-4 mol KMnO₄ / 0.0312 L KMnO₄ = 0.01 or 1x10^-2 M KMnO₄

Answer 1

Answer-

According to significant rules-

For addition/Subtraction -Add or Subtract in normal way and then round off the answer to the least number of decimal places in the problem.

For multiplication/division- Multiply or Divide in normal way and then round off the answer to the least precise among problem.

Given,

0.105 g Na₂C₂O₄ * (1 mol / 134 g Na₂C₂O₄) * (2 mol KMnO₄ / 5 mol Na₂C₂O₄) = ?

using significant rules

First solve,

1 mol / 134 g Na₂C₂O₄

Divide,

1 mol / 134 g Na₂C₂O₄ = 0.007 mol/gNa₂C₂O₄

Least precise is 1 which have 1 significant figure. So, answer is 7 * 10^-3 mol/gNa₂C₂O₄

Now, solve

2 mol KMnO₄ / 5 mol Na₂C₂O₄

Divide,

2 mol KMnO₄ / 5 mol Na₂C₂O₄ = 0.4 KMnO₄ /Na₂C₂O₄

Both are least precise and have 1 significant figure. So, answer is 4 *10^-1 KMnO₄ /Na₂C₂O₄

_{Put these in our problem,}

0.105 g Na₂C₂O₄ * 7 * 10^-3 mol/gNa₂C₂O₄ * 4 *10^-1 KMnO₄ /Na₂C₂O₄

_{Solve this,}

0.105 g Na₂C₂O₄ * 7 * 10^-3 mol/gNa₂C₂O₄ * 4 *10^-1 KMnO₄ /Na₂C₂O₄ = 3.94 * 10^-4mol KMnO₄ /Na₂C₂O₄

Least precise in problem have 1 significant figure .

So, our answer is 3 * 10^-4mol KMnO₄ /Na₂C₂O₄

Now ,

Solve,

3*10^-4 mol KMnO₄ / 0.0312 L KMnO₄ = 9.6 * 10^-3 M

But least precise have 1 significant figure. So, rounding off to 1 significant figure gives 0.01 M

Answer is 0.01 M or 1 * 10^-2 M which have 1 significant figure. The calculation of numeric part is correct.