Answer:
To solve this problem, we need to use the concept of stoichiometry, which is the calculation of the quantities of reactants and products in a chemical reaction. We also need to use the formula for concentration, which is the amount of solute divided by the volume of solution. Here are the steps to follow:
(a) Calculate the concentration, in mol/dm³, of the M₂CO₃ solution.
- First, we need to find the number of moles of HCl that reacted with M₂CO₃. We can use the given concentration and volume of HCl to do this. The formula is:
`moles of HCl = concentration of HCl x volume of HCl`
Substituting the values, we get:
`moles of HCl = 0.20 mol/dm³ x 30.00 cm³`
Since 1 dm³ = 1000 cm³, we need to convert the volume of HCl from cm³ to dm³ by dividing by 1000. We get:
`moles of HCl = 0.20 mol/dm³ x 0.03000 dm³`
Simplifying, we get:
`moles of HCl = 0.006 mol`
- Next, we need to find the number of moles of M₂CO₃ that reacted with HCl. We can use the balanced chemical equation to do this. The equation shows that for every 2 moles of HCl, 1 mole of M₂CO₃ reacts. Therefore, we can use the ratio of 2:1 to find the moles of M₂CO₃. The formula is:
`moles of M₂CO₃ = moles of HCl / 2`
Substituting the value, we get:
`moles of M₂CO₃ = 0.006 mol / 2`
Simplifying, we get:
`moles of M₂CO₃ = 0.003 mol`
- Finally, we need to find the concentration of M₂CO₃ in the solution. We can use the given mass and volume of M₂CO₃ solution to do this. The formula is:
`concentration of M₂CO₃ = moles of M₂CO₃ / volume of M₂CO₃ solution`
Substituting the values, we get:
`concentration of M₂CO₃ = 0.003 mol / 1000 cm³`
Again, we need to convert the volume from cm³ to dm³ by dividing by 1000. We get:
`concentration of M₂CO₃ = 0.003 mol / 1 dm³`
Simplifying, we get:
`concentration of M₂CO₃ = **0.003 mol/dm³**`
(b) Calculate the relative atomic mass of M and identify the metal M using the Periodic Table.
- First, we need to find the molar mass of M₂CO₃ using the given mass and moles. The formula is:
`molar mass of M₂CO₃ = mass of M₂CO₃ / moles of M₂CO₃`
Substituting the values, we get:
`molar mass of M₂CO₃ = 16.6 g / 0.003 mol`
Simplifying, we get:
`molar mass of M₂CO₃ = **5533 g/mol**`
- Next, we need to find the molar mass of CO₃ using the relative atomic masses from the Periodic Table. The formula is:
`molar mass of CO₃ = (relative atomic mass of C) + (3 x relative atomic mass of O)`
Substituting the values, we get:
`molar mass of CO₃ = (12 g/mol) + (3 x 16 g/mol)`
Simplifying, we get:
`molar mass of CO₃ = **60 g/mol**`
- Then, we need to find the molar mass of M using the molar masses of M₂CO₃ and CO₃. The formula is:
`molar mass of M = (molar mass of M₂CO₃ - molar mass of CO₃) / 2`
Substituting the values, we get:
`molar mass of M = (5533 g/mol - 60 g/mol) / 2`
Simplifying, we get:
`molar mass of M = **2736 g/mol**`
- Finally, we need to identify the metal M using its molar mass and the Periodic Table. We can look for an element that has a relative atomic mass close to or equal to **2736 g/mol**. The element that matches this criterion is **Rutherfordium (Rf)**, which has a relative atomic mass of **267 g/mol**. Therefore, the metal M is **Rutherfordium**.
Step-by-step explanation: