Question

Three solutions X,Y,Z of HCl are mixed to produce 100ml of 0.1 M solution. The molarities of X, Y, Z are 0.07M, 0.12M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed ?

Answer 1

Answer on Question #44099 - Chemistry - Other

Question:

Three solutions X, Y, Z of HCl are mixed to produce 100ml of 0.1 M solution. The molarities of X, Y, Z are 0.07M, 0.12M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Solution:

1. The amount of HCl in the resulting solution is the following:

$$c(\mathrm{HCl}) = \frac{n(\mathrm{HCl})}{V(\text{solution})}$$

Consequently

$$n(\mathrm{HCl}) = c(\mathrm{HCl}) \cdot V(\text{solution}) = \frac{100\ \mathrm{mL}}{1000} \cdot 0.1\ \frac{\mathrm{mol}}{\mathrm{L}} = 0.01\ \mathrm{mol}$$

2. The volume of HCl in every solution is marked with $x, y$ and $z$. We can write the equation:

$$V_{\Sigma}(\mathrm{HCl}) = V_{x}(\mathrm{HCl}) + V_{y}(\mathrm{HCl}) + V_{z}(\mathrm{HCl}) = x + y + z = 0.1\ \mathrm{L}$$

Or

$$x + y + z = 0.1$$

3. Then we write the formula for total amount of HCl:

$$\begin{array}{l} n_{\Sigma}(\mathrm{HCl}) = n_{x}(\mathrm{HCl}) + V_{y}(\mathrm{HCl}) + n_{z}(\mathrm{HCl}) = c_{\Sigma}(\mathrm{HCl}) \cdot n_{\Sigma}(\mathrm{HCl}) \\ = c_{x}(\mathrm{HCl}) \cdot n_{x}(\mathrm{HCl}) + c_{y}(\mathrm{HCl}) \cdot n_{y}(\mathrm{HCl}) + c_{z}(\mathrm{HCl}) \cdot n_{z}(\mathrm{HCl}) \\ = 0.07x + 0.12y + 0.15z = 0.01\ \mathrm{mol} \end{array}$$

Or

$$0.07x + 0.12y + 0.15z = 0.01\ \mathrm{mol}$$

Or

$$7x + 12y + 15z = 1$$

4. The elimination of variable $x$ it can be expressed by $y$, that is the solution $Z$ is substituted by $Y$ by way of coefficient expressed by ratio of respective molarities:

$$\frac{c_{z}(\mathrm{HCl})}{c_{y}(\mathrm{HCl})} = 1.25$$

Consequently,

$$z = 1.25y$$

5. The set of equations can be composed:

$$\left\{ \begin{array}{l} x + y + z = 0.1 \\ 7x + 12 + 15z = 1 \end{array} \right.$$

If $z = 1.25y$, then

$$\left\{ \begin{array}{l} x + y + 1.25y = 0.1 \\ 7x + 12y + 18.75y = 1 \end{array} \right.$$

Then

$$\left\{ \begin{array}{l} x + 2.25y = 0.1 \\ 7x + 30.75y = 1 \end{array} \right.$$ $$\left\{ \begin{array}{l} x = 0.1 - 2.25y \\ 7x + 30.75y = 1 \end{array} \right.$$

Then

$$\begin{array}{l} 7 \cdot (0.1 - 2.25y) + 30.75y = 1 \\ 0.7 - 15.75y + 30.75y = 1 \\ 15y = 0.3 \\ y = 0.02 \\ z = 1.25y = 0.025 \\ x = 0.1 - y - z = 0.1 - 0.02 - 0.025 = 0.055 \\ \end{array}$$

6. The volumes of solutions X, Y, Z are:

$$\begin{array}{l} V_x(\mathrm{HCl}) = 0.055\,L = 55\,mL \\ V_y(\mathrm{HCl}) = 0.025\,L = 25\,mL \\ V_z(\mathrm{HCl}) = 0.020\,L = 20\,mL \\ \end{array}$$

Answer: The volumes of X, Y, Z solutions are 0.055 L, 0.025 L and 0.020 L respectively.

http://www.AssignmentExpert.com/