Chapter 7: Problem 71
\(0.05\) mole of \(\mathrm{NaOH}\) is added to 5 litres of water. What will be the \(\mathrm{pH}\) of the solution? (a) 12 (b) 7 (c) 2 (d) 10
Short Answer
Expert verified
The pH of the solution is 12.
Step by step solution
01
Calculate the molarity of the NaOH solution
The molarity (M) of a solution is calculated by dividing the number of moles of solute by the volume of the solution in liters. In this exercise, we have 0.05 moles of NaOH added to 5 liters of water. Thus, the molarity of NaOH is given by Molarity = Moles of solute / Volume of solution in liters.
02
Calculate the concentration of hydroxide ions
Since NaOH is a strong base, it completely dissociates in water. Thus, the concentration of hydroxide ions ([OH^{-}]) is equal to the molarity of the NaOH solution.
03
Calculate the pOH of the solution
The pOH of a solution is calculated using the formula pOH = -log[OH^{-}]. Calculate the pOH by taking the negative logarithm (base 10) of the hydroxide ion concentration.
04
Calculate the pH of the solution
The pH and pOH of a solution are related by the equation pH + pOH = 14. Using the pOH obtained from the previous step, calculate the pH of the solution by subtracting the pOH from 14.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molarity
Molarity, often represented by the symbol 'M,' is a measure of concentration that indicates how many moles of a solute are present in one liter of a solution. This value is fundamentally important in chemistry because it allows for the precise measurement of substances for reactions and solutions.
For example, when you dissolve 0.05 moles of a substance, like NaOH (sodium hydroxide), into a certain volume of water – say 5 liters in this case – you can determine the molarity by using the formula: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]. Hence, the molarity of the NaOH solution would be \[ M = \frac{0.05 \text{ moles}}{5 \text{ liters}} = 0.01M \].
Understanding the concept of molarity is crucial because it sets the stage for further calculations, such as finding the concentration of ions in a solution after a strong base has dissociated.
For example, when you dissolve 0.05 moles of a substance, like NaOH (sodium hydroxide), into a certain volume of water – say 5 liters in this case – you can determine the molarity by using the formula: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]. Hence, the molarity of the NaOH solution would be \[ M = \frac{0.05 \text{ moles}}{5 \text{ liters}} = 0.01M \].
Understanding the concept of molarity is crucial because it sets the stage for further calculations, such as finding the concentration of ions in a solution after a strong base has dissociated.
Dissociation of Strong Base
When a strong base, such as NaOH, is dissolved in water, it dissociates completely into its constituent ions. In the case of NaOH, it separates into sodium ions (Na+) and hydroxide ions (OH-).
The complete dissociation is a key characteristic of strong bases and impacts the resulting pH of the solution. The equation representing this process is: \[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \].
Every mole of NaOH yields one mole of hydroxide ions. In our example, the 0.05 moles of NaOH added to 5 liters of water will produce the same number of moles of hydroxide ions. This complete dissociation is what makes it predictable to calculate properties like pH, as there is a direct relation between the amount of base added and the hydroxide ion concentration in the solution.
The complete dissociation is a key characteristic of strong bases and impacts the resulting pH of the solution. The equation representing this process is: \[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \].
Every mole of NaOH yields one mole of hydroxide ions. In our example, the 0.05 moles of NaOH added to 5 liters of water will produce the same number of moles of hydroxide ions. This complete dissociation is what makes it predictable to calculate properties like pH, as there is a direct relation between the amount of base added and the hydroxide ion concentration in the solution.
pOH
pOH is a measure of the hydroxide ion concentration in a solution, expressed on a logarithmic scale. Similar to pH, which is a measure of hydrogen ion concentration, pOH provides insights into the basicity of a solution. The relationship between hydroxide ion concentration and pOH is given by: \[ \text{pOH} = -\log[\text{OH}^-] \].
By calculating the pOH, you can understand how basic a solution is. The lower the pOH, the higher the concentration of hydroxide ions, and thus, the more basic the solution. In our scenario, after determining the concentration of hydroxide ions resulting from the dissociation of NaOH, we can easily calculate the pOH. This information then allows us to find the pH, as pH and pOH are interconnected.
By calculating the pOH, you can understand how basic a solution is. The lower the pOH, the higher the concentration of hydroxide ions, and thus, the more basic the solution. In our scenario, after determining the concentration of hydroxide ions resulting from the dissociation of NaOH, we can easily calculate the pOH. This information then allows us to find the pH, as pH and pOH are interconnected.
Hydroxide Ion Concentration
Hydroxide ion concentration ([OH-]) refers to the amount of hydroxide ions in a solution. It is directly related to both the molarity of a strong base and its dissociation in water. Since each molecule of a strong base like NaOH yields one hydroxide ion upon dissociation, the molarity of the base is equivalent to the hydroxide ion concentration.
In the example given, the molarity of the NaOH solution is 0.01M, which means the concentration of hydroxide ions is also 0.01M. This value is essential for determining the pOH and ultimately the pH of the solution, as it reflects the basic nature of the solution and is an integral part of the pH calculation process.
In the example given, the molarity of the NaOH solution is 0.01M, which means the concentration of hydroxide ions is also 0.01M. This value is essential for determining the pOH and ultimately the pH of the solution, as it reflects the basic nature of the solution and is an integral part of the pH calculation process.
