The $\text{pH}$ of an aqueous solution, which measures the concentration of hydrogen ions ($\text{H}^+$), is fundamentally dependent on temperature. The numerical $\text{pH}$ value of a solution changes if its temperature is altered. This relationship is crucial for accurate chemical analysis and stems from changes in the underlying chemical equilibrium within the water molecules.
The Shifting Neutral Point of Pure Water
A common belief is that a $\text{pH}$ value of exactly $7.0$ always represents a neutral solution. This is only accurate for pure water at a standard temperature of $25^\circ\text{C}$. Neutrality is chemically defined by the condition where the concentration of hydrogen ions ($\text{H}^+$) equals the concentration of hydroxide ions ($\text{OH}^-$).
As the temperature of pure water increases, its numerical $\text{pH}$ value decreases. For example, the $\text{pH}$ of neutral water is $7.0$ at $25^\circ\text{C}$, but it drops to approximately $6.14$ when heated to $100^\circ\text{C}$. Conversely, cooling pure water to $0^\circ\text{C}$ causes its neutral $\text{pH}$ value to rise to about $7.47$.
Despite these numerical shifts, the water remains chemically neutral at all temperatures. This occurs because the concentrations of $\text{H}^+$ and $\text{OH}^-$ ions remain equal to each other. The change in the $\text{pH}$ number merely reflects that the scale itself adjusts with temperature to maintain the condition of neutrality.
The Chemical Mechanism of Temperature Dependence
The change in the neutral $\text{pH}$ value is governed by the auto-ionization of water, where water molecules split into ions. This reaction is often simplified to the formation of $\text{H}^+$ and $\text{OH}^-$ ions. The extent to which this reaction occurs is described by the ion product of water, known as $K_w$.
Like all equilibrium constants, the value of $K_w$ is highly dependent on temperature. The auto-ionization of water is an endothermic reaction, meaning the process absorbs heat. When the temperature of the water is raised, the system responds by shifting the equilibrium to favor the products, according to Le Chatelier’s Principle.
This shift results in a greater number of both $\text{H}^+$ and $\text{OH}^-$ ions being produced. A higher concentration of $\text{H}^+$ ions directly translates to a lower $\text{pH}$ value, which is why the $\text{pH}$ of neutral water decreases as temperature rises. The $K_w$ value increases from $1.0 \times 10^{-14}$ at $25^\circ\text{C}$ to $4.99 \times 10^{-13}$ at $100^\circ\text{C}$, confirming the increased ionization.
Accurate $\text{pH}$ Measurement and Temperature Compensation
Temperature affects $\text{pH}$ measurement in two distinct ways, both requiring consideration for accurate results. The first is the actual chemical change in the solution’s hydrogen ion concentration ($K_w$ effect). The second is the physical effect of temperature on the glass electrode used in a $\text{pH}$ meter.
The electrode’s response is described by the Nernst equation, which includes a temperature variable ($\text{T}$) that determines the sensor’s electrical output per $\text{pH}$ unit. This means the electrical voltage generated by the electrode for a given $\text{pH}$ changes as the temperature fluctuates. For example, the ideal slope is $-59.16$ millivolts per $\text{pH}$ unit only at $25^\circ\text{C}$.
Modern $\text{pH}$ meters use Automatic Temperature Compensation ($\text{ATC}$) to account for this electrode-specific effect. The $\text{ATC}$ sensor measures the sample temperature and automatically adjusts the Nernst slope calculation. This correction ensures the meter accurately translates the millivolt reading into the correct $\text{pH}$ value at that specific temperature. However, $\text{ATC}$ only corrects for the electrode’s behavior and does not account for the actual, temperature-induced $\text{pH}$ change in the sample itself.
Real-World Effects in Solutions and Environments
While the auto-ionization of water provides a baseline effect, the $\text{pH}$ change in real-world solutions is further complicated by the presence of other chemicals.
Buffered Solutions
Solutions that contain a mix of a weak acid and its conjugate base are known as buffered solutions, such as human blood or many industrial fluids. In a buffered system, temperature change affects both the water’s $\text{K}_w$ and the acid dissociation constant ($\text{K}_a$) of the buffer components. The change in $\text{K}_a$ typically causes the $\text{pH}$ to decrease as the temperature rises, similar to pure water. However, the magnitude of the change is often smaller due to the buffer’s resistance to $\text{pH}$ shifts.
Dissolved Gases
Temperature also influences the solubility of dissolved gases, which can have a pronounced effect on the $\text{pH}$ of natural waters. Carbon dioxide ($\text{CO}_2$) dissolves in water to form carbonic acid, which lowers the $\text{pH}$. As the temperature of water warms, the solubility of $\text{CO}_2$ decreases, causing the gas to escape from the solution. This loss of $\text{CO}_2$ reduces the concentration of carbonic acid, which in turn causes the solution’s $\text{pH}$ to rise, demonstrating an effect opposite to the auto-ionization of water.