Calculating PH Of Solution Mixing NaOH And HCl

Jul 13, 2025 by ADMIN 47 views

Understanding pH Calculation: NaOH and HCl Reaction

The pH of a solution is a crucial concept in chemistry, indicating its acidity or alkalinity. To understand the pH, we often look at the concentration of hydrogen ions (H+) in a solution. A pH of 7 is considered neutral, values below 7 are acidic, and those above 7 are alkaline or basic. This article delves into a practical scenario: calculating the pH of a solution formed by mixing 50 mL of 0.1 M NaOH (sodium hydroxide) with 100 mL of 0.1 M HCl (hydrochloric acid). This involves understanding the principles of acid-base reactions and stoichiometry.

Neutralization Reaction: NaOH and HCl

When calculating the pH of a solution produced by mixing a strong acid like HCl and a strong base like NaOH, the key lies in understanding the neutralization reaction that occurs. Neutralization is the reaction between an acid and a base, which results in the formation of salt and water. In our specific case, sodium hydroxide (NaOH), a strong base, reacts with hydrochloric acid (HCl), a strong acid, according to the following balanced chemical equation:

NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)

This equation illustrates that one mole of NaOH reacts with one mole of HCl. This 1:1 stoichiometric ratio is crucial for determining the limiting reactant and the amount of excess reactant, which will ultimately dictate the pH of the resulting solution. In this reaction, the H+ ions from HCl react with the OH- ions from NaOH to form water (H2O), effectively neutralizing the solution. The other product, NaCl (sodium chloride), is a neutral salt and does not affect the pH. To accurately calculate the pH, we need to determine whether the acid or the base is in excess after the reaction. This involves calculating the number of moles of each reactant present initially. The reactant that is not completely consumed in the reaction will determine the final pH of the solution. If HCl is in excess, the solution will be acidic; if NaOH is in excess, the solution will be basic; and if they neutralize each other completely, the solution will be neutral, with a pH of 7.

Determining Moles of Reactants

To accurately determine the pH of the solution created by mixing NaOH and HCl, the initial step is to calculate the number of moles of each reactant present. The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. Therefore, to find the number of moles, we use the formula:

Moles = Molarity (M) × Volume (L)

For NaOH, we have 50 mL of 0.1 M solution. Converting the volume to liters (50 mL = 0.050 L), we can calculate the moles of NaOH:

Moles of NaOH = 0.1 M × 0.050 L = 0.005 moles

Similarly, for HCl, we have 100 mL of 0.1 M solution. Converting the volume to liters (100 mL = 0.100 L), the moles of HCl are calculated as:

Moles of HCl = 0.1 M × 0.100 L = 0.010 moles

These calculations show that we have 0.005 moles of NaOH and 0.010 moles of HCl. Comparing these values, we see that there are more moles of HCl than NaOH. This observation is critical because it indicates that HCl is in excess, and the resulting solution will be acidic. The next step is to determine how much HCl remains after reacting with all the NaOH. This excess HCl will dictate the final concentration of hydrogen ions (H+) in the solution, which is essential for calculating the pH. Understanding the initial quantities of each reactant is a fundamental aspect of stoichiometry and is crucial for predicting the outcome of chemical reactions.

Identifying the Limiting Reactant

In the reaction between NaOH and HCl, determining the limiting reactant is crucial for understanding the pH of the solution. The limiting reactant is the reactant that is completely consumed in a chemical reaction, thereby dictating the amount of product formed. In this scenario, it will help us determine how much of the other reactant, the excess reactant, remains after the reaction. As we established earlier, the balanced chemical equation for the reaction is:

NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)

This equation shows a 1:1 stoichiometric ratio between NaOH and HCl, meaning one mole of NaOH reacts with one mole of HCl. We calculated that we have 0.005 moles of NaOH and 0.010 moles of HCl. Since the reaction consumes NaOH and HCl in a 1:1 ratio, all 0.005 moles of NaOH will react with 0.005 moles of HCl. This means that NaOH will be completely used up in the reaction. Therefore, NaOH is the limiting reactant because it limits the amount of product that can be formed.

On the other hand, HCl is present in excess. To find out how much HCl is left after the reaction, we subtract the moles of HCl that reacted with NaOH from the initial moles of HCl. Understanding which reactant is limiting and which is in excess is essential for accurately predicting the final composition of the solution and, consequently, its pH. The excess reactant will determine the concentration of H+ ions in the solution, which is directly related to the pH value. The next step involves calculating the remaining moles of the excess reactant, which is HCl in this case.

Calculating Excess Reactant

After identifying NaOH as the limiting reactant in the reaction with HCl, the next crucial step in determining the pH of the solution is to calculate the amount of excess HCl remaining after the reaction. We initially had 0.010 moles of HCl, and we know that 0.005 moles of HCl reacted with the 0.005 moles of NaOH. To find the moles of HCl remaining, we subtract the reacted moles from the initial moles:

Moles of HCl remaining = Initial moles of HCl - Moles of HCl reacted Moles of HCl remaining = 0.010 moles - 0.005 moles = 0.005 moles

This calculation shows that 0.005 moles of HCl are left in the solution after the reaction. This excess HCl is what will determine the acidity of the final solution. To calculate the pH, we need to find the concentration of the remaining HCl in the total volume of the solution. The total volume is the sum of the volumes of the NaOH and HCl solutions that were mixed. We started with 50 mL of NaOH and 100 mL of HCl, so the total volume is:

Total volume = 50 mL + 100 mL = 150 mL

Converting this to liters, we have 150 mL = 0.150 L. Now that we have the moles of excess HCl and the total volume of the solution, we can calculate the concentration of HCl, which is equivalent to the concentration of H+ ions in the solution. This concentration is a key value in determining the pH. The accurate calculation of excess reactant is a pivotal step in understanding the final chemical environment of the solution and its implications for pH.

Determining the Concentration of H+ Ions

To accurately determine the pH of the solution, we need to calculate the concentration of hydrogen ions (H+) resulting from the excess HCl. We have already established that there are 0.005 moles of HCl remaining after the reaction with NaOH, and the total volume of the solution is 0.150 L. The concentration of HCl, which in this case is equal to the concentration of H+ ions because HCl is a strong acid and completely dissociates in water, can be calculated using the formula:

Concentration (M) = Moles / Volume (L)

Plugging in the values, we get:

[H+] = 0.005 moles / 0.150 L = 0.0333 M

This result indicates that the concentration of H+ ions in the solution is 0.0333 M. This concentration is critical because it directly correlates to the pH of the solution. A higher concentration of H+ ions signifies a more acidic solution, while a lower concentration indicates a more alkaline solution. Now that we have the concentration of H+ ions, we can proceed to calculate the pH using the pH formula. This step is the final quantitative determination of the acidity of the solution, providing a specific numerical value that characterizes its chemical properties. Understanding the relationship between excess acid concentration and H+ ion concentration is fundamental to mastering acid-base chemistry.

Calculating the pH

The final step in determining the pH of the solution after mixing NaOH and HCl is to use the concentration of H+ ions we calculated earlier. The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration. The formula for pH is:

pH = -log10[H+]

We found that the concentration of H+ ions, [H+], is 0.0333 M. Plugging this value into the formula, we get:

pH = -log10(0.0333)

Using a calculator to find the logarithm, we get:

pH ≈ -(-1.477)

pH ≈ 1.477

Therefore, the pH of the solution is approximately 1.477. This value indicates that the solution is highly acidic, which is expected since we had excess HCl after the neutralization reaction. The pH scale ranges from 0 to 14, with values less than 7 indicating acidity, 7 indicating neutrality, and greater than 7 indicating alkalinity. A pH of 1.477 is significantly lower than 7, confirming the acidic nature of the solution. This calculation demonstrates how the principles of stoichiometry and acid-base chemistry can be applied to determine the pH of a solution resulting from a chemical reaction. The pH value provides a quantitative measure of the acidity or basicity of the solution, which is crucial in various scientific and industrial applications.

In summary, determining the pH of a solution formed by mixing 50 mL of 0.1 M NaOH with 100 mL of 0.1 M HCl involves a series of steps rooted in stoichiometry and acid-base chemistry. First, we calculated the moles of each reactant to identify the limiting reactant and the excess reactant. Then, we determined the moles of excess HCl remaining after the reaction and calculated the concentration of H+ ions in the solution. Finally, using the pH formula, we calculated the pH to be approximately 1.477, indicating a highly acidic solution. This exercise illustrates the practical application of chemical principles in predicting the properties of solutions. Understanding these concepts is fundamental in various fields, including chemistry, biology, and environmental science, where pH plays a crucial role in many processes and reactions. The ability to calculate pH accurately is an essential skill for anyone working with chemical solutions, ensuring safe and effective handling and use.