Alright, let's solve this problem step-by-step.
Step 1: Understand the given information
1. We have a solution of [tex]\( X_2CO_3 \)[/tex] (a metal trioxocarbonate(IV)):
- 25.00 cm³ of the solution contains 1.86 g of the substance [tex]\( X_2CO_3 \)[/tex].
- The total volume of the solution is 250.00 cm³.
2. We have a hydrogen chloride solution:
- 27.00 cm³ of the solution.
- The concentration of HCl in this solution is 3.65 g per dm³.
Step 2: Calculate the concentration of the [tex]\( X_2CO_3 \)[/tex] solution
Since 1.86 g of [tex]\( X_2CO_3 \)[/tex] is present in 25.00 cm³ of the solution:
[tex]\[ \text{Concentration of } X_2CO_3 = \frac{\text{mass of } X_2CO_3}{\text{volume of solution}} = \frac{1.86 \text{ g}}{25.00 \text{ cm}^3} \][/tex]
[tex]\[ \text{Concentration of } X_2CO_3 = 0.0744 \text{ g/cm}^3 \][/tex]
Step 3: Equate this concentration to the total volume
Given the total volume of [tex]\( X_2CO_3 \)[/tex] solution is 250.00 cm³, the concentration remains the same at 0.0744 g/cm³.
Step 4: Calculate the mass of hydrogen chloride in the 27.00 cm³ of the HCl solution
First, convert the concentration of HCl from g/dm³ to g/cm³. Since 1 dm³ = 1000 cm³:
[tex]\[ \text{Concentration of HCl} = \frac{3.65 \text{ g}}{1000 \text{ cm}^3} \][/tex]
[tex]\[ \text{Concentration of HCl} = 0.00365 \text{ g/cm}^3 \][/tex]
Now, we calculate the mass of HCl in 27.00 cm³ of this solution:
[tex]\[ \text{Mass of HCl} = \text{Concentration} \times \text{Volume} \][/tex]
[tex]\[ \text{Mass of HCl} = 0.00365 \text{ g/cm}^3 \times 27.00 \text{ cm}^3 \][/tex]
[tex]\[ \text{Mass of HCl} = 0.09855 \text{ g} \][/tex]
Final Answer
The concentration of hydrogen chloride in g/cm³ is [tex]\( 0.00365 \, \text{g/cm}^3 \)[/tex].
The mass of hydrogen chloride that reacted is [tex]\( 0.09855 \, \text{g} \)[/tex].
