Which of the following solutions is alkaline?
Understanding Acidic, Basic, and Neutral Solutions
The question asks us to identify which of the given solutions is alkaline. Solutions can be classified as acidic, basic (alkaline), or neutral based on their hydrogen ion concentration, denoted as $[H^+]$. This concentration is directly related to the pH scale, which is commonly used to measure the acidity or alkalinity of a solution.
Defining Acidity, Alkalinity, and Neutrality based on [H⁺]
In pure water at a standard temperature of $25^\circ\text{C}$, there is a natural equilibrium where water molecules dissociate into hydrogen ions ($H^+$) and hydroxide ions ($OH^-$). The concentration of these ions is equal:
$$[H^+] = [OH^-] = 1 \times 10^{-7} \text{ Mol/l}$$
This is the point of neutrality. Based on this, we define the types of solutions:
- Neutral Solution: A solution where the concentration of hydrogen ions equals the concentration in pure water at $25^\circ\text{C}$.
- $[H^+] = 1 \times 10^{-7} \text{ Mol/l}$
- Acidic Solution: A solution where the concentration of hydrogen ions is higher than in pure water at $25^\circ\text{C}$. This means there are relatively more $H^+$ ions than $OH^-$ ions.
- $[H^+] > 1 \times 10^{-7} \text{ Mol/l}$
- Alkaline (Basic) Solution: A solution where the concentration of hydrogen ions is lower than in pure water at $25^\circ\text{C}$. This implies that the concentration of hydroxide ions ($[OH^-]$) is higher than $1 \times 10^{-7}$ Mol/l (since $[H^+][OH^-] = 1 \times 10^{-14}$ at $25^\circ\text{C}$). There are relatively more $OH^-$ ions than $H^+$ ions.
- $[H^+] < 1 \times 10^{-7} \text{ Mol/l}$
Analyzing the Given Options
Let's examine each option provided in the question based on the definitions above:
| Option | $[H^+]$ Value | Comparison to $1 \times 10^{-7}$ Mol/l | Type of Solution |
|---|---|---|---|
| 1 | $1 \times 10^{-4}$ Mol/l | $10^{-4}$ is greater than $10^{-7}$ ($10^{-4} > 10^{-7}$) | Acidic |
| 2 | $[H^+] < 1 \times 10^{-7}$ Mol/l | $[H^+]$ is less than $10^{-7}$ ($[H^+] < 10^{-7}$) | Alkaline |
| 3 | $[H^+] > 1 \times 10^{-7}$ Mol/l | $[H^+]$ is greater than $10^{-7}$ ($[H^+] > 10^{-7}$) | Acidic |
| 4 | $1 \times 10^{-7}$ Mol/l | $[H^+]$ is equal to $10^{-7}$ ($[H^+] = 10^{-7}$) | Neutral |
From the analysis, we can see that the solution with a hydrogen ion concentration $[H^+]$ less than $1 \times 10^{-7}$ Mol/l is classified as alkaline.
Conclusion on Alkaline Solution
Comparing our analysis with the options, Option 2, which states $[H^+] < 1 \times 10^{-7}$ Mol/l, correctly describes an alkaline solution according to the standard definition at $25^\circ\text{C}$.
Revision Table: Acidity, Neutrality, Alkalinity
| Solution Type | Hydrogen Ion Concentration ($[H^+]$) | pH Range |
|---|---|---|
| Acidic | $[H^+] > 1 \times 10^{-7}$ Mol/l | pH < 7 |
| Neutral | $[H^+] = 1 \times 10^{-7}$ Mol/l | pH = 7 |
| Alkaline (Basic) | $[H^+] < 1 \times 10^{-7}$ Mol/l | pH > 7 |
Additional Information: The pH Scale and $[H^+]$
The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. pH is defined as the negative common logarithm of the hydrogen ion concentration:
$$\text{pH} = -\log_{10}[H^+]$$
This formula shows the inverse relationship between $[H^+]$ and pH. As $[H^+]$ increases, pH decreases, indicating increasing acidity. Conversely, as $[H^+]$ decreases, pH increases, indicating increasing alkalinity.
- If $[H^+] = 1 \times 10^{-7}$, $\text{pH} = -\log(10^{-7}) = 7$.
- If $[H^+] = 1 \times 10^{-4}$, $\text{pH} = -\log(10^{-4}) = 4$ (Acidic).
- If $[H^+] = 1 \times 10^{-9}$, $\text{pH} = -\log(10^{-9}) = 9$ (Alkaline). Note that $10^{-9}$ is less than $10^{-7}$.
Understanding the relationship between hydrogen ion concentration and the pH scale is fundamental to classifying solutions as acidic, neutral, or alkaline.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
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1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
