Chapter 4: Problem 124
Calculate the concentration of all ions present when 0.160 \(\mathrm{g}\) of \(\mathrm{MgCl}_{2}\) is dissolved in 100.0 \(\mathrm{mL}\) of solution.
Short Answer
Expert verified
When 0.160 g of MgCl鈧 is dissolved in 100.0 mL of solution, the concentration of Mg虏鈦 ions is 0.0168 M, and the concentration of Cl鈦 ions is 0.0336 M.
Step by step solution
01
Convert grams of MgCl鈧 to moles.
To find the moles of MgCl鈧 dissolved, we must first convert the 0.160 g of MgCl鈧 to moles. Using the molar mass of MgCl鈧, which can be found by adding the molar masses of Mg (24.31 g/mol) and two Cl atoms (2 x 35.45 g/mol):
Molar mass of MgCl鈧 = 24.31 g/mol + (2 x 35.45 g/mol) = 95.21 g/mol
Now, convert the mass of MgCl鈧 to moles using the molar mass:
Moles of MgCl鈧 = (0.160 g) / (95.21 g/mol) = 0.00168 mol
02
Calculate the moles of Mg虏鈦 and Cl鈦 ions produced.
When MgCl鈧 dissolves, it produces one mole of Mg虏鈦 ions and two moles of Cl鈦 ions for each mole of MgCl鈧. Therefore, we can find the moles of Mg虏鈦 and Cl鈦 ions produced as follows:
Moles of Mg虏鈦 = Moles of MgCl鈧 = 0.00168 mol
Moles of Cl鈦 = 2 x Moles of MgCl鈧 = 2 x 0.00168 mol = 0.00336 mol
03
Convert the volume of the solution to liters.
The volume of the solution is given in milliliters (mL), and we need to convert it to liters (L) to calculate the molar concentration. To do this, divide the volume in milliliters by 1000:
Volume in liters = 100.0 mL / 1000 = 0.100 L
04
Calculate the concentration of Mg虏鈦 and Cl鈦 ions.
Now we can find the concentration of Mg虏鈦 and Cl鈦 ions in the solution by dividing the moles of each ion by the volume of the solution in liters:
Concentration of Mg虏鈦 = Moles of Mg虏鈦 / Volume in liters = 0.00168 mol / 0.100 L = 0.0168 M
Concentration of Cl鈦 = Moles of Cl鈦 / Volume in liters = 0.00336 mol / 0.100 L = 0.0336 M
Therefore, when 0.160 g of MgCl鈧 is dissolved in 100.0 mL of solution, the concentration of Mg虏鈦 ions is 0.0168 M, and the concentration of Cl鈦 ions is 0.0336 M.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Molarity
When dealing with solutions in chemistry, a common way to express the concentration is through molarity. Molarity is defined as the number of moles of solute (the substance being dissolved) per liter of solution.
In formula terms, it's represented as:\( M = \frac{n}{V} \)where \( n \) is the number of moles of solute, and \( V \) is the volume of solution in liters.
Concentration of Mg虏鈦 is 0.0168 M.
This directly tells us how many moles of magnesium ions are present per litre of the solution.
In formula terms, it's represented as:\( M = \frac{n}{V} \)where \( n \) is the number of moles of solute, and \( V \) is the volume of solution in liters.
- Molarity helps us understand how concentrated a solution is.
- Higher molarity means a more concentrated solution with more solute particles per unit volume.
- It is expressed in units of moles per liter (M).
Concentration of Mg虏鈦 is 0.0168 M.
This directly tells us how many moles of magnesium ions are present per litre of the solution.
Ion Dissolution Process
Ion dissolution is the process where ionic compounds, like \( \text{MgCl}_2 \), separate into their respective ions in a solution.
This is a critical concept in understanding how ions interact in water and influence the solution's properties.When \( \text{MgCl}_2 \) dissolves in water:- It dissociates into one \( \text{Mg}^{2+} \) ion and two \( \text{Cl}^- \) ions.- The dissolution equation is represented as:\[ \text{MgCl}_2 (s) \rightarrow \text{Mg}^{2+} (aq) + 2 \text{Cl}^- (aq) \]
This is a critical concept in understanding how ions interact in water and influence the solution's properties.When \( \text{MgCl}_2 \) dissolves in water:- It dissociates into one \( \text{Mg}^{2+} \) ion and two \( \text{Cl}^- \) ions.- The dissolution equation is represented as:\[ \text{MgCl}_2 (s) \rightarrow \text{Mg}^{2+} (aq) + 2 \text{Cl}^- (aq) \]
- Ionic compounds dissolve to form a solution with free ions capable of conducting electricity, often known as an electrolytic solution.
- The molar relationships in dissolution help in calculating the resulting ion concentrations, as seen by multiplying the moles of compound by the number of ions produced.
Chemical Calculations in Solutions
Chemical calculations are essential to comprehend solutions and their specific characteristics.
Calculations typically involve converting mass to moles, determining volume in liters, and understanding reaction stoichiometry.Here's how the process plays out step by step:
Calculations typically involve converting mass to moles, determining volume in liters, and understanding reaction stoichiometry.Here's how the process plays out step by step:
- Mass to Moles: Use the molar mass to convert the mass of a compound to moles, as seen in the conversion of 0.160 g of \( \text{MgCl}_2 \) to 0.00168 mol.
- Volume Conversion: Convert the volume of solution from mL to liters for use in molarity calculations. For example, 100.0 mL equals 0.100 L.
- Moles of Ions: Based on the stoichiometry of dissolution, calculate the amount of each ion present.