Question

Atmospheric CO \(_{2}\) levels have risen by nearly 20\(\%\) over the past 40 years from 320 ppm to 400 ppm. (a) Given that the average \(\mathrm{pH}\) of clean, unpolluted rain today is \(5.4,\) determine the pH of unpolluted rain 40 years ago. Assume that carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) formed by the reaction of \(\mathrm{CO}_{2}\) and water is the only factor influencing pH. $$\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{CO}_{3}(a q)$$ (b) What volume of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and 1.0 \(\mathrm{atm}\) is dissolved in a 20.0 -L bucket of today's rainwater?

Short answer

\(pH_{40 Years Ago} = - log[H_{2}CO_{3 (40 Years Ago)}] = - log[\frac{80}{100} \times 10^{-5.4}]\) moles of CO₂ = \([10^{-5.4}] \times 20.0 L\) V = (moles of CO₂) × (0.0821 L atm K⁻¹ mol⁻¹) × (298.15 K)

Step-by-step solution

Find the concentration of H₂CO₃ today.

Since the pH of unpolluted rain today is 5.4, we can find the concentration of H₂CO₃(Assuming no other factor affects pH) using the formula: pH = - log[H⁺] (where H⁺ represents the concentration of H⁺ ions) Now, we can find the concentration of H⁺ ions: \[H^{+} = 10^{-pH}\] \[H^{+} = 10^{-5.4}\]

Calculate the concentration of H₂CO₃, 40 years ago.

Since atmospheric CO₂ levels have risen by nearly 20% over the past 40 years, we can assume that the concentration of H₂CO₃ was 20% less in the past. Therefore, we'll calculate the concentration of H₂CO₃ 40 years ago: \[H_{2}CO_{3 (40 Years Ago)} = \frac{80}{100} \times H^{+}\]

Determine the pH of unpolluted rain 40 years ago.

Now that we have the concentration of H₂CO₃ 40 years ago, we can determine the pH by using the formula: pH = - log[H⁺] \[pH_{40 Years Ago} = - log[H_{2}CO_{3 (40 Years Ago)}]\]

Calculate the number of moles of CO₂ in today's rainwater.

To find the number of moles of CO₂ dissolved in today's rainwater, we'll need to use the concentration of H₂CO₃, which we found in step 1, and the volume of rainwater, which is 20.0 L. We'll use the following formula: moles of CO₂ = [H⁺] × volume of rainwater moles of CO₂ = [H⁺] × 20.0 L

Determine the volume of CO₂ at 25°C and 1.0 atm.

We can use the ideal gas law to find the volume of CO₂ at 25°C and 1.0 atm. The ideal gas law is defined as follows: PV = nRT (where P is pressure, V is volume, n is moles of gas, R is the ideal gas constant, and T is temperature in Kelvin) First, convert the temperature to Kelvin: T = 25°C + 273.15 = 298.15 K Now, plug in the values into the ideal gas law: (1.0 atm) × V = (moles of CO₂) × (0.0821 L atm K⁻¹ mol⁻¹) × (298.15 K) To find the volume, V, divide both sides by 1.0 atm: V = (moles of CO₂) × (0.0821 L atm K⁻¹ mol⁻¹) × (298.15 K)

Key concepts

Atmospheric CO2 levels

The concentration of carbon dioxide (CO2) in the atmosphere is a crucial environmental metric that directly affects the acidity of rainwater. Over the past few decades, human activities like fossil fuel combustion and deforestation have led to a significant increase in atmospheric CO2 levels. The given exercise uses a real-world example to illustrate this point, showing that over a span of 40 years, CO2 has increased from 320 parts per million (ppm) to 400 ppm. This roughly 20% rise has important implications for the environment, particularly in terms of the pH of rainwater, an indicator of its acidity.

An increase in CO2 levels leads to more CO2 dissolving into rainwater, forming carbonic acid (H2CO3), a weak acid, which lowers the pH of rain, making it more acidic. The alteration of the natural carbon cycle can lead to acid rain, which has negative effects on aquatic life, vegetation, and infrastructure. Understanding how CO2 levels impact rainwater's pH is essential in environmental studies and helps us evaluate the human impact on the planet's ecosystems.

Carbonic acid in rainwater

Carbonic acid plays a pivotal role in determining the pH of rainwater. When CO2 gas from the atmosphere dissolves in water, it reacts with water to form carbonic acid, through the reversible reaction: \[CO_{2}(g) + H_{2}O(l) \rightleftharpoons H_{2}CO_{3}(aq)\]. This process occurs naturally but is enhanced by the increased levels of CO2 due to human activity.

Carbonic acid is a weak acid, meaning that it partially dissociates in water to release hydrogen ions (H+), which are responsible for acidity. The balance between CO2, carbonic acid, and the dissociation into hydrogen and bicarbonate ions is delicate and is described by an equilibrium expression, which is subject to change with the CO2 concentration. A higher concentration of atmospheric CO2 shifts this equilibrium, leading to more carbonic acid in rainwater and thus a lower pH value. It is a perfect example of how the chemistry of the atmosphere can impact the chemistry of natural waters.

Calculating pH from H+ concentration

The pH is a scale used to quantify the acidity or basicity of an aqueous solution. It is calculated as the negative logarithm (base 10) of the hydrogen ion concentration. The formula is expressed as \[ pH = -\log[H^+] \]. In simpler terms, if we know how many hydrogen ions are present in a solution, we can calculate the pH, giving us an idea of how acidic the rainwater is.

For instance, in the provided exercise, the current pH of rainwater is 5.4. Using the formula, we convert this into the hydrogen ion concentration by reversing the logarithmic function: \[H^+ = 10^{-5.4}\]. Understanding the direct relationship between H+ concentration and pH is essential for students since it allows them to connect a tangible property, the pH value, to the more abstract concept of ionic concentration. Calculating the change in pH over time due to shifts in atmospheric CO2 illustrates the dynamic nature of environmental chemistry and its measurable effects on our ecosystem.