Question

A \(25.27\)-g sample of pure sodium was prepared for an experiment. How many \(\mathrm{mL}\) of sodium is this? (Density of sodium is \(0.97 \mathrm{~g} / \mathrm{mL}\).)

Short answer

The volume of the sodium sample is approximately 26.06 mL.

Step-by-step solution

Understand the Given Data

Identify the given values in the problem. The mass of the sodium sample is 25.27 grams, and the density of sodium is 0.97 grams per milliliter.

Recall the Formula for Density

Density is given by the formula \ \ \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] \ \ Rearrange this formula to solve for volume: \ \ \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Substitute the Values

Plug the given values into the rearranged formula. \ \ \[ \text{Volume} = \frac{25.27 \text{ grams}}{0.97 \text{ grams per milliliter}} \]

Calculate the Volume

Perform the division to find the volume: \ \ \[ \text{Volume} = \frac{25.27}{0.97} \approx 26.06 \text{ milliliters} \]

Key concepts

mass

Mass is a fundamental property of matter that measures the amount of substance in an object. It is typically measured in grams (g) for small quantities or kilograms (kg) for larger quantities. In this exercise, the mass of the sodium sample is given as 25.27 grams. Understanding mass is crucial in calculations involving density, as it helps determine the volume of a substance when its density is known.

volume

Volume refers to the amount of space that a substance or object occupies. For liquids and gases, volume is commonly measured in liters (L) or milliliters (mL). In the context of this exercise, we need to determine the volume of sodium based on its mass and density. Volume can be calculated using the rearranged density formula: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]. In our exercise, with a mass of 25.27 grams and a density of 0.97 grams per milliliter, you can find the volume by dividing the mass by the density.

density formula

The density formula is a vital concept in chemistry and physics for understanding how much mass is contained in a given volume of a substance. The formula is expressed as: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]. This formula helps us understand the relationship between mass and volume. In this exercise, we rearrange the formula to solve for volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]. Using the given values, the calculation becomes: \[ \text{Volume} = \frac{25.27 \text{ grams}}{0.97 \text{ grams per milliliter}} \]. This allows us to determine the volume of sodium required.

chemistry problem solving

Solving chemistry problems often involves understanding and manipulating various formulas and units. Here are some steps to effectively solve such problems:

• Identify the given data and units. In this example, we know the mass (25.27 grams) and the density (0.97 grams per milliliter).
• Recall and understand the relevant formula. For this problem, it's the density formula \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \].
• Rearrange the formula to solve for the desired variable. Here, we rearrange to find the volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \].
• Substitute the known values into the formula and perform the calculation: \[ \text{Volume} = \frac{25.27 \text{ grams}}{0.97 \text{ grams per milliliter}} = 26.06 \text{ milliliters} \].
• Check your units and reasoning to ensure the answer makes sense. The calculation correctly converts the mass of sodium to its volume using the provided density.

Using these steps can help you tackle various chemistry problems more systematically.