The chemistry of rainwater is influenced by both seawater and other sources, depending on where and when it rains. In coastal areas, seawater plays a significant role in providing sodium, chloride, magnesium, and sulfate ions to rainwater. This is because sea spray and evaporation contribute to the formation of rain clouds. However, rainwater also contains chemicals from terrestrial sources like dust, soil, rocks, plants, animals, and human activities. These include calcium, potassium, ammonium, nitrate, fluoride, and organic acids. The proportions of these chemicals vary depending on weather conditions, distance from the sea, wind direction, topography, and pollution levels in the atmosphere.
It's important to note that rainwater chemistry is not identical to seawater chemistry. Instead, it is a complex mixture of different components that reflect the air and environmental quality. Seawater has a much higher salinity than rainwater, meaning it contains more dissolved salts per liter of water. On average, seawater has a salinity of 3.5%, while rainwater has a salinity of less than 0.1%. Additionally, seawater is more alkaline with a higher pH value. The average pH of seawater is 8.1, whereas rainwater has an average pH of 5.6. The pH of rainwater can be influenced by acidic pollutants like sulfur dioxide and nitrogen oxides, which can cause acid rain.
Rain water begins as pure (distilled) water produced by evaporation of sea water. It absorbs gases and aerosols from the air mainly CO2 which forms carbonic acid and makes it acidic. Other atmospheric gases, which are both natural and anthropogenic, such as sulphur dioxide and NOx also affect its acidity and chemisty.
Sea water has a chemisty produced by river water which contains dissolved minerals owing to the acidity of rain water. However, the chemisty of river water is distinct from that of sea water because of the chemical processes which occur in the oceans.
I must correct you; the carbon system is not a closed cycle, although the hydrological system is. There are sources into the carbon system from volcanoes and fossil fuel burning, and sinks on land from the burial of organic material e.g. peat, and in the ocean from the deposits of carbonate sediments.