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The theoretical minimum energy required to capture one kg of CO₂ from the atmosphere in 2024 is 440.75 kJ

Summary​

The minimum energy needed to capture atmospheric CO₂ is fundamentally limited by thermodynamics, calculated using Gibbs free energy. At 2024 atmospheric concentrations (420 ppm), this requires at least 440.75 kJ per kg of CO₂ captured. While higher CO₂ concentrations (like 900 ppm projected for 2100) reduce this minimum to 397.55 kJ/kg, current technologies require significantly more energy due to real-world inefficiencies. This calculation uses room temperature (300K) and ideal gas assumptions to determine the energy needed to concentrate CO₂ from atmospheric levels to pure form. These thermodynamic limits apply regardless of capture technology and highlight the inherent challenges of direct air capture.

The main barrier to large-scale adoption of atmospheric carbon dioxide removal and, more specifically, Direct Air Capture (DAC) is the high energy requirement in the sorbent desorption/regeneration phase. Many recent breakthroughs in DAC technology have focused on minimizing the energy requirement, increasing the efficiency of the process, or using low-quality heat sources to regenerate the sorbent material. However, no matter which technology is used, including technologies that will not be invented for decades into the future, there will always be a theoretical minimum energy requirement for capturing and containing carbon dioxide that cannot be circumvented. This theoretical minimum energy requirement is defined by the property of Gibbs free energy.

What is the Gibbs free energy?​

As atmospheric carbon dioxide is in its gaseous state, energy needs to be expended in order to move a molecule that is in a low concentration to a high concentration. Many gases have a natural tendency to stay dispersed in the air. If it were not for this natural tendency, pockets of carbon dioxide or oxygen might form in the atmosphere which is not the case.

Gibbs free energy is a complex concept that can be hard to visualize or form analogies using real-world examples, as it is based on a number of assumptions and describes idealized conditions that often don't occur naturally, such as 100% efficient and reversible energy conversion. However, it is a useful concept to understand the thermodynamic limits as it provides a benchmark for the absolute minimum amount of energy required to capture CO₂.

Calculating the minimum energy requirement​

As already stated, the whole process of DAC and storage can be simplified to one fundamental task: moving CO₂ that is in a low concentration in the air to a high concentration where it can be stored or transported. Gibbs free energy is defined as the measure of the maximum reversible work that can be performed by a system at constant temperature and pressure. The expression for Gibbs free energy of mixing is defined as follows:

ΔG=RTln⁡(yCO2,highyCO2,low)\begin{align*} \Delta \text{G} &= RT\ln\left(\frac{y_{\text{CO}_2\text{,high}}}{y_{\text{CO}_2\text{,low}}}\right) \end{align*}

Where:

  • ΔG\Delta \text{G} is the Gibbs free energy
  • RR is the ideal gas constant (8.314 J/mol·K)
  • TT is the temperature
  • yCO2,highy_{\text{CO}_2\text{,high}} Final mole fraction of CO₂ (e.g., in concentrated form).
  • yCO2,lowy_{\text{CO}_2\text{,low}} Initial mole fraction of CO₂ in air.

We can make some basic assumptions to show how this equation can be used to calculate the minimum energy requirement for capturing CO₂. If we assume:

  • The system is operating around room temperature of 300K (approximately 27°C or 80°F).
  • The temperature and pressure in the system remain constant throughout the process.
  • There are no efficiency losses in the system, i.e., 100% efficient.
  • The initial mole fraction of CO₂ in air is 420 ppm or 0.00042. This is the concentration of CO₂ in the atmosphere as of December 2024.
  • The final mole fraction of CO₂ in air is 1, which is 100% pure CO₂.

Therefore, we can calculate the minimum theoretical energy required per mole of CO₂ as follows:

ΔG=RTln⁡(yCO2,highyCO2,low)=8.314×300×ln⁡(10.00042)=8.314×300×ln⁡(2380.952)=8.314×300×7.775=19393 J/mol=19.393 kJ/mol\begin{align*} \Delta \text{G} &= RT\ln\left(\frac{y_{\text{CO}_2\text{,high}}}{y_{\text{CO}_2\text{,low}}}\right)\\ &= 8.314 \times 300 \times \ln\left(\frac{1}{0.00042}\right)\\ &= 8.314 \times 300 \times \ln(2380.952)\\ &= 8.314 \times 300 \times 7.775\\ &= 19393 \text{ J/mol}\\ &= 19.393 \text{ kJ/mol} \end{align*}

Using Gibbs free energy, the theoretical minimum energy required to capture one mole of CO₂ is 19.393 kJ 1. This value is reported in moles, which is a fundamental unit of measurement for the amount of a substance used in chemistry. Instead, we can convert this value to a more practical unit of measurement, such as kJ/kg of CO₂. We can calculate the mass of one mole of CO₂ by adding the molar mass of all the atoms. CO₂ contains one carbon atom and two oxygen atoms with the molar mass:

  • Carbon: 12.011 g/mol
  • Oxygen: 15.999 g/mol
ΔMolar Mass=12.011+2×15.999=44.009 g/mol\begin{align*} \Delta \text{Molar Mass} &= 12.011 + 2 \times 15.999\\ &= 44.009 \text{ g/mol} \end{align*}

Therefore, the mass of one mole of CO₂ is approximately 44 g. So from the previous calculations, we can calculate the theoretical minimum energy required to capture one kg of CO₂ as follows:

ΔEnergy=19.393 kJ/mol44 g/mol×1000 g=440.75 kJ/kg\begin{align*} \Delta \text{Energy} &= \frac{19.393 \text{ kJ/mol}}{44 \text{ g/mol}} \times 1000 \text{ g}\\ &= 440.75 \text{ kJ/kg} \end{align*}

Calculating the minimum energy requirement for different concentrations.​

One of the main difficulties that makes carbon capture so difficult is its extremely small concentration in the atmosphere of just 420 ppm. This makes capturing carbon similar to finding a needle in a haystack. However, it is easier to capture CO₂ from the air if the concentration is increased. For example, if we use the atmospheric concentration of 900 ppm, which is the estimated atmospheric concentration of CO₂ in 2100 under the IPCC's RCP 8.5 pathway, which considers the "carry on as usual" scenario where very little is done to address climate change, we can calculate the minimum energy required to capture one kg of CO₂ as follows 2:

ΔG=RTln⁡(yCO2,highyCO2,low)=8.314×300×ln⁡(10.0009)=8.314×300×ln⁡(1111.11)=8.314×300×7.013=17492 J/mol=17.492 kJ/mol\begin{align*} \Delta \text{G} &= RT\ln\left(\frac{y_{\text{CO}_2\text{,high}}}{y_{\text{CO}_2\text{,low}}}\right)\\ &= 8.314 \times 300 \times \ln\left(\frac{1}{0.0009}\right)\\ &= 8.314 \times 300 \times \ln(1111.11)\\ &= 8.314 \times 300 \times 7.013\\ &= 17492 \text{ J/mol}\\ &= 17.492 \text{ kJ/mol} \end{align*}

So at a concentration of 900 ppm, the theoretical minimum energy required to capture one kg of CO₂ from the air and separate it into pure CO₂ is:

ΔEnergy=17.492 kJ/mol44 g/mol×1000 g=397.55 kJ/kg\begin{align*} \Delta \text{Energy} &= \frac{17.492 \text{ kJ/mol}}{44 \text{ g/mol}} \times 1000 \text{ g}\\ &= 397.55 \text{ kJ/kg} \end{align*}

Sources​

Footnotes​

  1. House, K. Z., Baclig, A. C., Ranjan, M., van Nierop, E. A., Wilcox, J., & Herzog, H. J. (2011). Economic and energetic analysis of capturing CO₂ from ambient air. Proceedings of the National Academy of Sciences of the United States of America, 108(51), 20428-20433. https://doi.org/10.1073/pnas.1012253108 ↩

  2. Intergovernmental Panel on Climate Change (IPCC). (2023). Climate change 2023: Synthesis report. Contribution of Working Groups I, II, and III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Core Writing Team, H. Lee, & J. Romero, Eds.). IPCC. https://doi.org/10.59327/IPCC/AR6-9789291691647 ↩