Question

Calculate the molarity of a solution obtained by mixing \(250 \mathrm{ml}\) of \(0.5 \mathrm{M}\) HCl with \(750 \mathrm{ml}\) of \(2 \mathrm{M}\) HCl. (a) \(1.8\) (b) \(2.0\) (c) \(1.6\) (d) \(0.8\)

Short answer

(a) 0.5 (b) 1.0 (c) 1.6 (d) 2.0 Answer: (c) 1.6

Step-by-step solution

Write down the given information

We know the initial molarities and volumes of the two HCl solutions: \(M_1\) = \(0.5\mathrm{M}\) \(V_1\) = \(250\mathrm{ml}\) \(M_2\) = \(2\mathrm{M}\) \(V_2\) = \(750\mathrm{ml}\)

Calculate the final volume

Sum the initial volumes to find the final volume: \(V_f = V_1 + V_2 = 250\mathrm{ml} + 750\mathrm{ml}\) \(V_f = 1000\mathrm{ml}\)

Use the formula to find the final molarity

Plug the initial molarities and volumes, along with the final volume, into the formula: \(M_1V_1 + M_2V_2 = M_fV_f\) \((0.5\mathrm{M})(250\mathrm{ml}) + (2\mathrm{M})(750\mathrm{ml}) = M_f(1000\mathrm{ml})\)

Solve for the final molarity

Divide both sides of the equation by 1000 ml to solve for the final molarity: \(M_f = \frac{(0.5\mathrm{M})(250\mathrm{ml}) + (2\mathrm{M})(750\mathrm{ml})}{1000\mathrm{ml}}\) \(M_f = \frac{125\mathrm{mmol} + 1500\mathrm{mmol}}{1000\mathrm{ml}}\) \(M_f = \frac{1625\mathrm{mmol}}{1000\mathrm{ml}}\) \(M_f = 1.625\mathrm{M}\) Since the nearest answer provided is 1.6, the correct response is (c) 1.6.

Key concepts

Solution Concentration

Solution concentration refers to how much solute is present in a given quantity of solvent or solution. It's a way to convey how strong or weak a solution is. The concentration can be expressed in various units, but in chemistry, molarity is one of the most popular.
The concentration tells you how much active ingredient you have, in terms of moles, within a certain volume. Understanding concentration is critical because it helps predict how reactions will proceed. If the concentration is high, you might expect a faster reaction speed.

• Concentration Units: These include molarity (M), mass percent, volume percent, and more. In molarity, the concentration is expressed as moles of solute per liter of solution.
• Importance: Definition of concentration helps in quantitative preparation and analysis of chemical solutions.

Chemical Mixing

Chemical mixing involves combining two or more substances to form a new solution. When mixing solutions, the key is how the quantities and concentrations combine to form a new concentration.
Mixing can influence the physical and chemical properties of a solution. When different solutions are mixed, understanding the initial concentrations and volumes allows you to predict the resulting solution concentration.

• Changes in Properties: Chemical mixing may change properties like pH, color, and concentration.
• Reactions: Inconsistent or incorrect mixing can lead to undesirable reactions. Thus, calculating the expected outcome is essential in laboratory preparation.
• Homogenization: Ensures that the mixture is uniform, meaning the solute is evenly distributed throughout the solvent.

Molarity Formula

The molarity formula is an essential tool in chemistry for solution preparation and analysis. It helps in determining the molarity of a solution after combining different solutions or adding solute.
The molarity (\(M\)) is calculated using the formula:\[ M = \frac{n}{V} \]where \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters.
For mixing two solutions, the formula derives from the principle of conservation of moles:\[ M_fV_f = M_1V_1 + M_2V_2 \]Here, \(M_f\) is the final molarity, \(V_f\) is the total final volume, and \(M_1, V_1\) and \(M_2, V_2\) are the initial molarities and volumes of the two solutions.

• Calculation Steps: Rearrange the above equation to solve for the desired variable whether it's the final molarity or initial volumes and molarities.
• Practical Use: Useful in labs to predict the behavior of combined chemical solutions precisely.