Chapter 1: Problem 27
The density of water at \(40^{\circ} \mathrm{C}\) is \(0.992 \mathrm{~g} / \mathrm{mL}\). What is the volume of \(27.0 \mathrm{~g}\) of water at this temperature?
Short Answer
Expert verified
The volume is approximately 27.220 mL.
Step by step solution
Over 22 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass and Volume Relationship
Understanding the relationship between mass and volume is fundamental when working with concepts like density. Mass is the amount of matter in an object and is typically measured in units like grams (g) or kilograms (kg). Volume, on the other hand, describes the amount of space that an object occupies and is typically measured in units like milliliters (mL) or liters (L).
Linking mass and volume together, density allows us to understand how much matter is packed into a given volume of space. A denser substance will have more mass in the same volume compared to a less dense substance. In the context of our exercise, water's density at 40°C helps us relate its mass to its volume, enabling precise calculations.
Linking mass and volume together, density allows us to understand how much matter is packed into a given volume of space. A denser substance will have more mass in the same volume compared to a less dense substance. In the context of our exercise, water's density at 40°C helps us relate its mass to its volume, enabling precise calculations.
Density Formula
The density formula is a key tool in connecting mass and volume. It is presented mathematically as \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula tells us how much mass of a substance is contained in a given volume.
If we have the values for both mass and volume, we can calculate the density directly. Conversely, if we know the density and either the mass or volume, we can rearrange the formula to find the missing quantity. This flexibility makes the density formula versatile when solving various kinds of problems involving mass and volume.
In our specific problem, knowing the density of water at 40°C and its mass allows us to effectively determine the water's volume.
If we have the values for both mass and volume, we can calculate the density directly. Conversely, if we know the density and either the mass or volume, we can rearrange the formula to find the missing quantity. This flexibility makes the density formula versatile when solving various kinds of problems involving mass and volume.
In our specific problem, knowing the density of water at 40°C and its mass allows us to effectively determine the water's volume.
Volume Calculation
To find the volume when we have mass and density, we simply need to rearrange the density formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). This gives us a straightforward way to calculate the space that a given amount of substance occupies under specific conditions.
Using the values provided in the exercise, we determined the volume of 27.0 grams of water by substituting the mass (27.0 g) and the density of water at 40°C (0.992 g/mL) into the equation. The calculation \( \text{Volume} = \frac{27.0}{0.992} \approx 27.220 \ \text{mL} \) gives us the result. Thus, at 40°C, 27.0 grams of water occupies approximately 27.220 mL.
Using the values provided in the exercise, we determined the volume of 27.0 grams of water by substituting the mass (27.0 g) and the density of water at 40°C (0.992 g/mL) into the equation. The calculation \( \text{Volume} = \frac{27.0}{0.992} \approx 27.220 \ \text{mL} \) gives us the result. Thus, at 40°C, 27.0 grams of water occupies approximately 27.220 mL.
Density of Water at 40°C
The density of water changes with temperature, which is important when performing calculations involving physical properties. At 40°C, the density of water is approximately 0.992 g/mL. This specific value is crucial for accurately determining the volume of water or related calculations at this temperature.
This temperature variation is because as water heats, the molecules move more vigorously and spread slightly apart, lowering the density.
Having the correct density value is essential for the accuracy of any calculations, such as the one performed in our exercise, ensuring that we consider the specific characteristics of water at different temperatures.
This temperature variation is because as water heats, the molecules move more vigorously and spread slightly apart, lowering the density.
Having the correct density value is essential for the accuracy of any calculations, such as the one performed in our exercise, ensuring that we consider the specific characteristics of water at different temperatures.
