Question

The density of mercury is \(13.6 \mathrm{~g} / \mathrm{mL}\). Express the density in SI units \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\).

Short answer

The density of mercury in SI units is 13600 kg/m³.

Step-by-step solution

Understand the Problem

We are asked to convert the density of mercury from grams per milliliter (g/mL) to kilograms per cubic meter (kg/m³). This requires understanding the relationship between the units.

Convert Grams to Kilograms

Since 1 gram (g) is equal to 0.001 kilograms (kg), to convert the density from grams to kilograms, multiply by 0.001. Thus, \[ 13.6 ext{ g/mL} = 13.6 imes 0.001 ext{ kg/mL} = 0.0136 ext{ kg/mL}. \]

Convert Milliliters to Cubic Meters

Since 1 milliliter (mL) is equal to \( 1 imes 10^{-6} \) cubic meters (m³), we convert milliliters to cubic meters. Therefore, \[ 0.0136 ext{ kg/mL} = \frac{0.0136 ext{ kg}}{1 imes 10^{-6} ext{ m}^3}. \]

Calculate the Density in kg/m³

Perform the calculation by dividing 0.0136 by \( 1 imes 10^{-6} \). Thus, \[ 0.0136 ext{ kg/mL} = \frac{0.0136}{1 imes 10^{-6}} ext{ kg/m³} = 13600 ext{ kg/m³}. \]

Key concepts

Density Calculation

Density is a measure of how much mass is contained in a given volume. It tells us how tightly matter is packed together. To calculate density, you need to know two things: the object's mass and its volume. The formula for density is:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]Imagine you have a block of an unknown material. To find its density, you would weigh the block to get its mass and then measure its size to determine its volume. Once you have these two numbers, simply use the formula to find the density.

• If you have mass in kilograms and volume in cubic meters, the density will be in kilograms per cubic meter \(\text{(kg/m³)}\).
• If the mass is in grams and volume in milliliters, the density will be in grams per milliliter \(\text{(g/mL)}\).

Calculating density is crucial for understanding the properties of substances in physics and chemistry. Different materials have distinct densities, helping to identify them. So, the next time you hold a mysterious metal object, you'll understand how scientists can determine what it is just by using its density.

SI Units

SI units, or the International System of Units, are the standard units used in science worldwide. They ensure everyone speaks the same measurement language, much like how grammar rules help us communicate in English. The main idea behind SI units is universality. For example, instead of saying someone's height in feet and inches or centimeters, we'll use meters. This consistency helps scientists all over the world share and compare their research effectively.Key features of SI units include:

• Base units: like the meter \((\text{m})\) for length and the kilogram \((\text{kg})\) for mass.
• Derived units: like meters per second \((\text{m/s})\) for speed, deriving from the base units.

Using SI units prevents confusion. When learning about density in SI terms, like kilograms per cubic meter \((\text{kg/m³})\), you're using a derived unit that combines both mass (kilograms) and volume (cubic meters) into a single useful measure.

Metric System

The metric system is a decimal-based system of measurement used by most countries in the world. It's logically structured and makes calculations straightforward due to its reliance on base ten. At the core of the metric system is its simplicity.

• The base unit for length is the meter \((\text{m})\).
• The base unit for mass is the gram \((\text{g})\).
• The base unit for volume is the liter \((\text{L})\).

Each unit can be easily converted to a larger or smaller unit by moving the decimal point, thanks to prefixes like kilo- (for a thousand units), centi- (for one hundredth of a unit), or milli- (for one thousandth of a unit).For example, converting grams to kilograms involves moving the decimal point three places to the left. Similarly, moving from milliliters to liters also involves shifting the decimal by three places to the left.Understanding and using the metric system in calculations, like density conversions, can help students make sense of measurements quickly and accurately. This ability is not just useful in exams but also in real-world applications like cooking, construction, and engineering.