Problem 123 - Chemistry Matter and Change

Question

You are given a liquid of unknown density. The mass of a graduated cylinder containing 2.00 mL of the liquid is 34.68 g. The mass of the empty graduated cylinder is 30.00 g. Given this information, determine the density of the liquid. (Chapter 2)

Step-by-Step Solution

Answer

The density of the liquid can be determined by first finding the mass of the liquid, which is 4.68 g (34.68 g - 30.00 g). With the given volume of 2.00 mL (0.002 L), the density can be calculated using the formula, density = mass/volume, which results in a density of 2340 g/L.

Step 1: Determine the mass of the liquid

To find the mass of the liquid, subtract the mass of the empty graduated cylinder from the mass of the graduated cylinder containing the liquid. Mass of liquid = Mass of graduated cylinder containing liquid - Mass of empty graduated cylinder Mass of liquid = 34.68 g - 30.00 g

Step 2: Calculate the mass of the liquid

Subtract the two masses to find the mass of the liquid. Mass of liquid = 4.68 g

Step 3: Find the volume of the liquid

The volume of the liquid is given in the problem. Volume of liquid = 2.00 mL

Step 4: Convert the volume of the liquid to liters

Although the density can be calculated using mL, usually it's expressed in g/L for consistency. To convert mL to L, divide the volume by 1000. Volume of liquid in L = 2.00 mL / 1000 Volume of liquid in L = 0.002 L

Step 5: Calculate the density of the liquid

Determine the density of the liquid using the formula, density = mass/volume. Density of liquid = (4.68 g) / (0.002 L)

Step 6: Find the density of the liquid

Divide the mass of the liquid by its volume to find the density. Density of liquid = 2340 g/L The density of the liquid is 2340 g/L.

Key Concepts

Mass and Volume

Understanding the concepts of mass and volume is integral to solving many scientific problems, especially when working with the matter's physical properties. Mass is a measure of the amount of matter in an object and is often measured in grams (g) or kilograms (kg).

Volume, on the other hand, measures the amount of space an object or substance occupies. It is typically quantified in liters (L), milliliters (mL), or cubic meters. The relationship between mass and volume is crucial when you're calculating the density of a substance, which is a measure of how much mass is contained in a given volume. As seen in the exercise, knowing how to find and differentiate both mass and volume allows you to progress toward the calculation of density.

Unit Conversion

Unit conversion is a fundamental skill in science, because measurements can be taken and reported in various units, and working with consistent units is essential for accurate calculations. For instance, in the exercise provided, the volume of liquid was initially reported in milliliters (mL) and then converted to liters (L).

To convert volume from milliliters to liters, you divide the number of milliliters by 1000, since there are 1000 milliliters in a liter. Similarly, other unit conversions may be required in different scenarios, such as converting grams to kilograms by dividing by 1000, or converting feet to meters where a more comfortable conversion factor is used. Remember, when doing these conversions, keeping track of your units is as crucial as the numerical computations.

Density Formula

The density formula is a mathematical equation that is used to calculate an object's density, which is defined as its mass per unit volume. The formula is simple but powerful: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). In the context of the exercise, after finding the mass of the liquid to be 4.68 g and converting the volume to 0.002 L, the density is calculated by simply dividing the mass by the volume.

The ability to apply the density formula correctly and understanding its components is essential for scientists and engineers. Not only does it help in identifying substances and their purity, but it is also critical in designing objects to float or sink, calculating buoyancy, and even in more complex applications such as fluid dynamics. Hence, grasping the density calculation is a key step in mastering material properties and their applications.