To tackle this problem, we need to understand the reactions that occur when sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3) are titrated with hydrochloric acid (HCl) using different indicators. Each indicator changes color at different pH levels, which affects the volume of acid consumed in each titration.
Understanding the Reactions
When Na2CO3 is titrated with HCl, the reaction can be represented as follows:
- Na2CO3 + 2 HCl → 2 NaCl + H2O + CO2
This reaction shows that one mole of Na2CO3 reacts with two moles of HCl. Therefore, if we denote the volume of HCl used to reach the endpoint with phenolphthalein as V1, the amount of Na2CO3 in the mixture can be calculated based on this volume.
On the other hand, when NaHCO3 is titrated with HCl, the reaction is:
- NaHCO3 + HCl → NaCl + H2O + CO2
Here, one mole of NaHCO3 reacts with one mole of HCl. If we denote the volume of HCl used to reach the endpoint with methyl orange as V2, the amount of NaHCO3 can be determined from this volume.
Analyzing the Statements
Now, let's evaluate the options provided:
- (A) M(Na2CO3) = 10V1: This statement is incorrect. The molarity of Na2CO3 cannot be directly equated to 10 times the volume of HCl used in the titration with phenolphthalein. The stoichiometry indicates that 1 mole of Na2CO3 reacts with 2 moles of HCl, so the relationship would involve a factor of 2, not 10.
- (B) V2 > V1: This statement is true. Since Na2CO3 requires 2 moles of HCl for complete reaction, the volume of HCl used (V1) will be less than that used for NaHCO3 (V2), which only requires 1 mole of HCl. Therefore, V2 must be greater than V1.
- (C) M(NaHCO3) = 10(V2 - V1): This statement is also incorrect. The molarity of NaHCO3 cannot be expressed as 10 times the difference between V2 and V1. The relationship between the moles of NaHCO3 and the volume of HCl used is linear, not scaled by a factor of 10.
- (D) All are correct: Since we have already identified that statements A and C are incorrect, this option cannot be true.
Conclusion
Based on the analysis, the only true statement is (B) V2 > V1. This reflects the stoichiometric differences in the reactions of Na2CO3 and NaHCO3 with HCl. Understanding these relationships is crucial for accurately interpreting titration results and the underlying chemistry involved.
