A 1.8 gram sample of HCl is added to enough water to make 5.5 L of solution. What is the pH of this solution at 25 °C? Be sure to use at least 4 significant figures throughout your calculations; you can only be off by 0.1 pH units. Note: Due to the constraints of Canvas, please assume that all numerical values were given with 4 significant figures.
Answer (2)
Calculate the number of moles of HCl: 36.46 g/mol 1.8 g = 0.049369 mol .
Calculate the molarity of the HCl solution: 5.5 L 0.049369 mol = 0.008976 M .
Determine the concentration of H+ ions: [ H + ] = 0.008976 M .
Calculate the pH of the solution: p H = − l o g 10 ( 0.008976 ) = 2.0469 . Therefore, the pH is 2.05 .
Explanation
Problem Analysis We are given that 1.8 grams of HCl is added to enough water to make 5.5 L of solution. We need to find the pH of this solution at 25 °C. We will first calculate the number of moles of HCl, then the molarity of the solution, and finally the pH.
Calculating Moles of HCl First, we calculate the number of moles of HCl using its molar mass, which is approximately 36.46 g/mol: m o l es = m o l a r _ ma ss ma ss = 36.46 g/mol 1.8 g = 0.049369 mol (using 4 significant figures)
Calculating Molarity of HCl Next, we calculate the molarity of the HCl solution: M o l a r i t y = v o l u m e m o l es = 5.5 L 0.049369 mol = 0.008976 M (using 4 significant figures)
Determining [H+] Concentration Since HCl is a strong acid, it completely dissociates in water. Therefore, the concentration of H+ ions is equal to the molarity of the HCl solution: [ H + ] = 0.008976 M
Calculating pH Finally, we calculate the pH of the solution using the formula: p H = − l o g 10 [ H + ] = − l o g 10 ( 0.008976 ) = 2.0469 Rounding to two decimal places, the pH of the solution is approximately 2.05.
Final Answer Therefore, the pH of the solution is approximately 2.05.
Examples
The concept of pH calculation is crucial in various real-world applications. For instance, in environmental science, it's used to monitor the acidity of rainwater or soil, which affects plant growth and aquatic life. In medicine, understanding pH levels in the body is essential for diagnosing and treating certain conditions. Similarly, in the food industry, pH control is vital for preserving food and ensuring its safety. By calculating the pH of a solution, we can determine its acidity or alkalinity, which helps in making informed decisions in these diverse fields. For example, if the concentration of H + ions in a sample of rainwater is 2.5 × 1 0 − 5 M, then the pH of the rainwater is − l o g 10 ( 2.5 × 1 0 − 5 ) = 4.60 , indicating it is slightly acidic.
To find the pH of a 1.8 g HCl solution in 5.5 L of water, we first calculate the moles of HCl, which gives us a molarity of approximately 0.008976 M. The final pH, calculated from the concentration of hydrogen ions, is approximately 2.05. HCl is a strong acid and dissociates completely in solution, leading to this pH level.
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