Question

What is the mass of 275 L of seawater if the density is \(1.025 \mathrm{~g} / \mathrm{cm}^{3} ?\)

Short answer

The mass of 275 L of seawater is 281875 grams.

Step-by-step solution

Understand the Given Values

We are given the volume of seawater as 275 L and its density as \(1.025 \text{ g/cm}^3\). We need to find the mass of seawater using these values.

Convert Liters to Cubic Centimeters

Since the density is given in \(\text{g/cm}^3\), we should convert the volume from liters to cubic centimeters (\(\text{cm}^3\)). Remember that \(1 \text{ L} = 1000 \text{ cm}^3\). So, \(275 \text{ L} = 275 \times 1000 \text{ cm}^3 = 275000 \text{ cm}^3\).

Use the Formula for Mass

The general formula for mass is \( \text{mass} = \text{density} \times \text{volume} \). Substitute the known values into this formula to find the mass:\[\text{mass} = 1.025 \text{ g/cm}^3 \times 275000 \text{ cm}^3\]

Calculate the Mass

Perform the calculation from Step 3:\[\text{mass} = 1.025 \times 275000 = 281875 \text{ g}\]This means the mass of the seawater is 281875 grams.

Key concepts

Understanding Volume Conversion

When you're dealing with measurements in different units, sometimes it's necessary to convert from one unit of volume to another. Volume conversion is important in calculations where units need to match, especially when working with density.

• In the given exercise, we begin with a volume of seawater measured in liters.
• Since the density is provided in grams per cubic centimeter, we need to convert the volume from liters to cubic centimeters (cm³).

To make this conversion, remember that 1 liter is equivalent to 1000 cubic centimeters. Therefore, multiplying the number of liters by 1000 allows you to convert it to cm³. In this problem:

• 275 liters becomes 275,000 cubic centimeters because \(275 \times 1000 = 275,000\).

Understanding this conversion is crucial when handling density-related problems because it directly affects both the calculation of mass and the coherence of the units being used.

Applying the Mass Formula

The mass formula is a straightforward relationship that connects mass, density, and volume. It is foundational in calculating the mass of any substance:

• The mass formula is expressed as \( \text{mass} = \text{density} \times \text{volume} \).

Understanding each component is key:

• **Density** tells us how much mass exists per unit volume. In this problem, it is given as \(1.025 \text{ g/cm}^3\).
• **Volume** must be appropriately converted to match the units of density. Here, it is 275,000 cm³ after conversion from liters.
• **Mass** is what we calculate by using the formula.

By multiplying the density by the volume,

• we calculate the mass as \(1.025 \text{ g/cm}^3 \times 275,000 \text{ cm}^3 = 281,875 \text{ g}\).

Using the mass formula becomes intuitive through practice and helps in solving a variety of real-world physics and chemistry problems.

Mastering Unit Conversion

Understanding unit conversion is essential in many scientific calculations.It involves switching from one unit of measure to another, ensuring that multiply operations make sense and results are coherent.

• **Essential principle:** Units must be compatible for calculations. This often requires converting units beforehand.
• In density problems, this usually involves matching units of volume with those given for density (e.g., cm³ with g/cm³).

When converting units:

• Identify which units need conversion (e.g., liters to cubic centimeters here).
• Use known equivalencies, like \(1 \text{ L} = 1000 \text{ cm}^3\).

By maintaining consistent units, calculations flow smoothly, and results are reliable. Proper unit conversion avoids errors in interpreting the values of calculations, making this skill indispensable.