A glass containing \(345 \mathrm{~mL}\) of a soft drink (a carbonated beverage) was left sitting out on a kitchen counter. If the \(\mathrm{CO}_{2}\) released at room temperature \(\left(25^{\circ} \mathrm{C}\right)\) and pressure \((1 \mathrm{~atm})\) occupies \(1.40 \mathrm{~L}\), at a minimum, what is the concentration (in ppm) of the \(\mathrm{CO}_{2}\) in the original soft drink? (Assume the density of the original soft drink is \(0.965 \mathrm{~g} / \mathrm{mL}\).)

When it comes to measuring very dilute concentrations of substances, the term parts per million (ppm) plays a crucial role. It represents how many units of solute are contained in one million units of solution. To put this in perspective, 1 ppm is analogous to one minute in two years, or one drop of a substance in about 50 liters.

Specifically, in a chemical context, ppm defines the mass of a chemical or contaminate per unit volume of water. This can also be related to milligrams of the substance in one liter of water (mg/L). Given that ppm is a ratio, it is a dimensionless quantity. Hence, no matter what units are used for the individual measures, as long as they are the same, the ppm value is a consistent measure of concentration.

Points to Remember

• ppm is a measure of concentration.
• It is useful for very low concentration levels.
• It is equivalent to mg of solute per liter of solution for aqueous solutions.

Density is defined as the mass per unit volume of a substance, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). When it comes to solutions, density helps us calculate the mass of the solution if the volume is known, as seen in our example problem with the soft drink.

Concentration, on the other hand, is all about the amount of solute within a solvent. While density remains consistent irrespective of the amount, concentration can change depending on the volume of solvent used to dissolve the solute. The concentration can be expressed in multiple ways including molarity, molality, and as we have seen in this context, ppm.

Key Takeaways:

• Density helps determine mass from volume.
• Concentration reflects how much solute exists within a solvent.
• Both density and concentration are essential in calculating substances in ppm.

Gas volume conversion is an essential process in chemistry that involves converting the volume of a gas from one set of conditions (usually measured in liters or cubic meters) to another, often under standard temperature and pressure conditions (STP). For our example, the CO2 released from the soft drink was measured in liters, which had to be converted to milliliters (mL) to match the units of density for the concentration calculation.

It is also important to keep in mind that gases are less dense than liquids and solids, and their volume can be greatly affected by temperature and pressure. In the problem at hand, we assume room temperature and pressure, which simplifies our calculations. However, if conditions were different, we would need to employ the ideal gas law to find the exact volume at those conditions.

Practical Tip:

• Always ensure units are consistent when converting volumes for gas substances.
• Temperature and pressure significantly affect gas volumes.
• Knowing the correct conditions is critical for accurate conversions.

Solving chemical problems often involves a systematic approach that requires understanding and correctly applying scientific concepts and mathematical equations. The process we've observed in the soft drink example demonstrates a multi-step problem where each part builds on the previous, starting from volume conversion to calculating mass, and finally determining concentration in ppm.

Effective chemical problem-solving includes careful unit conversions, proper assumptions (like the density of CO2 in this problem), and rigorous attention to detail with the chemical properties involved. To tackle these problems, a structured approach and a clear understanding of the underlying chemistry are indispensable.

Guidelines for Tackling Chemical Problems:

• Understand the chemical principles related to the problem.
• Carry out step-by-step calculations meticulously.
• Ensure all units are consistent throughout the problem.
• Double-check calculations to avoid errors.