Question

Convert an energy of \(526 \mathrm{cal}\) to units of joules.

Short answer

The energy in joules is approximately \(2199.984 \, Joules\).

Step-by-step solution

Understand the conversion factor

The first step is to understand the conversion factor between calories and joules. One calorie (\(1 \, cal\)) is equal to approximately \(4.184 \, Joules\).

Apply the conversion factor

The next step is to apply the conversion factor to the given energy. We can do this by simply multiplying the given energy in calories by the conversion factor. Hence, \(526 \, cal = 526 \times 4.184 \, Joules\).

Key concepts

Calories to Joules

When you are converting energy from calories to joules, you're essentially changing one unit of energy measure to another. Understanding this conversion is very important in chemistry and physics as both units are used in different contexts.
To express calories in joules, we use a simple mathematical relationship: that one calorie is equal to approximately 4.184 joules. This means anytime you have a value in calories, you can find its equivalent in joules by multiplying it by 4.184.
This conversion is crucial when dealing with energy changes in chemical reactions or when calculating energy consumption. It helps bridge the gap between the science of nutrition, which often uses calories, and physics or chemistry that often deals with joules.

Conversion Factor

A conversion factor is a numerical value that is used to convert a measurement expressed in one set of units to another set of units. The concept of conversion factors is useful when translating between different systems or dimensions in science.
To convert from calories to joules, the conversion factor is 4.184. This is a constant value and it signifies how many joules one calorie contains. Using conversion factors makes calculations easier, since you just multiply the original measurement by the right conversion factor.

• Identify the units you want to convert from and to.
• Find the conversion factor between these units.
• Multiply the original value by the conversion factor to get the converted value.

This approach ensures precision and consistency in scientific calculations, particularly in chemistry calculations where appropriate unit conversions are often necessary for accurate results.

Chemistry Calculations

Chemistry calculations often involve conversions as they deal with various measurements and dimensions. Converting energy units like calories to joules is a common task. In chemistry, understanding energy conversions is essential when analyzing reactions that release or absorb energy.
Practically, when engaging in chemistry calculations, it is important to not only know the conversion factors but to apply them correctly. For example, when converting 526 calories into joules, you would calculate it as follows:
\[ 526 imes 4.184 = 2200.384 ext{ Joules} \]
Firstly, you identify the conversion factor—here, 4.184. Then, multiply it by the given number of calories to find the energy in joules.
This systematic process is a cornerstone of solving chemistry problems accurately, ensuring all data is in a manageable and comparable form throughout your calculations.