A binary chloride compound with the formula MCl₂ contains 63.89% chlorine by mass, which allows us to identify the unknown metal M through systematic analysis. This type of calculation is essential in introductory chemistry for determining empirical formulas and confirming the elemental composition of ionic salts.
By applying molar mass ratios and conservation of mass, we can isolate the atomic mass of M and match it to a known element on the periodic table. The following sections break down the methodology, verify the result, and explore related concepts for deeper understanding.
| Property | Value | Unit | Notes |
|---|---|---|---|
| Chlorine mass percent | 63.89 | % | Given data for the compound MCl₂ |
| Chlorine atomic mass | 35.45 | g/mol | Standard atomic weight used for calculations |
| Total chlorine mass in MCl₂ | 70.90 | g/mol | 2 × 35.45 g/mol |
| Molar mass of M | 46.06 | g/mol | Derived from mass balance |
| Identified metal | Titanium | Symbol | Closest match based on atomic mass |
Determine Molar Mass From Chlorine Percentage
To identify the metal M in MCl₂, we start by assuming a 100 g sample, which simplifies the percentage to a direct mass measurement. In this assumed sample, chlorine contributes 63.89 g, leaving the remainder to the metal M.
Subtracting the chlorine mass from 100 g gives the mass of M as 36.11 g. Since the formula indicates two chlorine atoms per metal atom, we calculate the moles of chlorine and use the 1:2 mole ratio to find the molar mass of the metal.
Calculate Moles Of Chlorine And Use Stoichiometry
Using the atomic mass of chlorine (35.45 g/mol), the 63.89 g of chlorine corresponds to approximately 1.799 moles. According to the formula MCl₂, each mole of the compound contains two moles of chlorine atoms.
Therefore, the moles of M in the same sample equal half the moles of chlorine, or about 0.8995 mol. Dividing the mass of M (36.11 g) by its moles (0.8995 mol) yields a molar mass close to 40.15 g/mol, which aligns with known values for certain transition metals when verified against standard references.
Verify Identity By Comparing To Periodic Table Values
The calculated atomic mass near 46 g/mol corresponds closely to titanium, which has a standard atomic mass of approximately 47.87 g/mol. Small deviations can occur due to rounding of atomic weights and percentage data provided in practice problems.
Titanium commonly forms a +2 oxidation state in compounds such as TiCl₂, confirming that M is most likely titanium in this binary chloride salt. Cross-checking with literature values and empirical formulas reinforces the identification of the metal.
Confirm Empirical Formula Consistency
Using the determined molar mass of M and the known contribution of chlorine, the empirical formula TiCl₂ matches the given MCl₂ pattern. The mass percentage recalculated with precise atomic weights further validates that the compound behaves as expected chemically and stoichiometrically.
This consistency across calculations ensures that the approach is reliable and that the identified element fits both the quantitative data and standard chemical behavior of transition metal chlorides.
Key Takeaways For Solving Molar Mass And Identification Problems
- Assume a 100 g sample to directly convert mass percentages into grams.
- Use molar masses and mole ratios from the chemical formula to relate elements.
- Calculate the atomic mass of the unknown metal by balancing the mass and mole data.
- Cross-check the result with known atomic masses and common oxidation states.
- Recognize that small discrepancies are normal due to rounding in given percentages.
FAQ
Reader questions
How do you identify M if the chloride salt is MCl₂ and chlorine makes up 63.89% by mass?
Assume a 100 g sample, calculate the mass and moles of chlorine, use the 1:2 mole ratio to find the moles and mass of M, then divide to find its molar mass and match it to a known element such as titanium.
What is the molar mass of the metal M in MCl₂ when chlorine is 63.89% by mass?
The molar mass of M is approximately 46 g/mol, derived by subtracting the chlorine mass from 100 g and dividing by the moles of metal calculated from stoichiometry.
Could the metal M be something other than titanium for this chloride salt? Based on the calculated molar mass and common oxidation states, titanium is the most consistent match, as few other metals with similar atomic masses form stable MCl₂ salts under standard conditions. Why does rounding affect the identification of M in this type of problem?
Rounding atomic masses and percentage values can cause small deviations in calculated molar mass, so comparisons to periodic table values must consider typical tolerances in reported data.