Question

What is the molarity of \(\mathrm{CO}_{2}\) in a liter of ocean water at \(25^{\circ} \mathrm{C}\) that contains approximately \(280 \mathrm{ppm}\) of \(\mathrm{CO}_{2} ?\) The density of ocean water is \(1027 \mathrm{kg} / \mathrm{m}^{3}\).

Short answer

The molarity of CO2 in ocean water at 25 °C containing approximately 280 ppm of CO2 is 0.00636 M.

Step-by-step solution

Understand the given information

The ocean water contains approximately 280 parts per million (ppm) of CO2. This means for every 1 million parts of solution, there are 280 parts of CO2. The density of ocean water is given as 1027 kg/m^3.

Convert ppm unit to grams

280 ppm of CO2 is equivalent to 280 mg of CO2 in 1kg (or 1 liter) of water. To have the amount of CO2 in grams, divide by 1000: \(280 \, \text{ppm} = 280 \, \text{mg/kg} = 280/1000 \, \text{g} = 0.28 \, \text{g}\)

Calculate moles of CO2

Use the molar mass of CO2 to convert grams to moles. The molar mass of CO2 is approximately 44.01 g/mol. Divide the mass by molar mass: \(0.28 \, \text{g} / 44.01 \, \text{g/mol} = 0.00636 \, \text{moles}\)

Calculate molarity

Finally, calculate the molarity of CO2 by using the definition of molarity, which is the moles of solute per liter of solution. Hence divide the moles by the volume in liters. As 1 kg of water is approximately equal to 1 liter, divide the moles by 1 liter to obtain the molarity: \(0.00636 \, \text{moles/L} = 0.00636 \, \text{M}\)

Key concepts

PPM to Grams Conversion

Parts per million, or ppm, is a way to express very dilute concentrations of substances. When dealing with solutions, understanding how to convert ppm to grams is crucial. PPM is a ratio that expresses how many parts of a solute are in a million parts of the solution. In this case, 280 ppm of \(\mathrm{CO}_2\) in ocean water means there are 280 parts of \(\mathrm{CO}_2\) per million parts of ocean water. To convert ppm to grams, consider that 1 ppm is equivalent to 1 milligram of solute in 1 liter (or 1 kilogram) of water. Thus, 280 ppm of \(\mathrm{CO}_2\) converts to 280 milligrams in 1 kilogram of ocean water. Since 1 kilogram is also 1 liter under standard conditions, 280 mg equates to 0.28 grams, as dividing by 1000 mg transforms milligrams into grams. This step is essential for the following calculations that require the weight in grams rather than ppm.

Moles Calculation

The calculation of moles is a fundamental concept in chemistry. Moles are a measure of quantity that allow chemists to convert between the mass of a substance and the number of molecules or atoms it contains. To determine the number of moles from grams, we use the molar mass of the substance. For \(\mathrm{CO}_2\), the molar mass is determined by adding together the atomic masses of carbon (approximately 12.01 g/mol) and oxygen (approximately 16.00 g/mol each), resulting in a molar mass of about 44.01 g/mol.
Once you know this, you can find the number of moles by dividing the mass of \(\mathrm{CO}_2\) in grams by its molar mass. In our example, with 0.28 grams of \(\mathrm{CO}_2\), we perform the division
\[\frac{0.28\, \text{g}}{44.01\, \text{g/mol}} \approx 0.00636 \text{ moles}\]
This result allows us to understand how many moles of \(\mathrm{CO}_2\) are present in the sample, and is a critical step for calculating molarity.

Density of Ocean Water

Density is a property of matter that represents mass per unit volume. For ocean water, the density is given as 1027 kg/m³. This means every cubic meter of ocean water has a mass of 1027 kilograms. Density can vary slightly based on factors like temperature and salinity, making it an important factor when dealing with solutions like the ocean. For problems concerning molarity, like this one, knowing the density allows us to equate volumes with masses under the assumption water’s density equates 1 liter with 1 kilogram due to practicality in calculations.
In practice, a density of 1027 kg/m³ implies that 1 liter of ocean water weighs about 1.027 kilograms. However, for simplicity and common practice, unless minute precision is required, 1 kg is often approximately 1 liter. Understanding the density of ocean water helps us properly interpret "liter equivalent" volumes in conversion calculations, ensuring accurate solutions in broader contexts, like the calculation of molarity.