Question

The specific heat capacity of graphite is \(0.71 \mathrm{~J} / \mathrm{g}\). C . Calculate the energy required to raise the temperature of 2.4 moles of graphite by 25.0 ".

Short answer

The energy required to raise the temperature of 2.4 moles of graphite by 25.0 degrees Celsius is \(511 \: \mathrm{J}\).

Step-by-step solution

Find the molar mass of graphite

Since graphite is made of carbon atoms, the molar mass of graphite is the same as the molar mass of carbon. Carbon has a molar mass of 12.01 g/mol.

Convert moles to mass

We are given that there are 2.4 moles of graphite. To convert moles to mass, multiply the number of moles by the molar mass: \[mass = moles * molar\:mass = 2.4\:moles * 12.01\:g/mol = 28.824\:g\]

Use the energy formula

Use the energy formula with the values obtained: \[E = mc∆T\] Here, m = 28.824 g, c = 0.71 J/g°C, and ∆T = 25°C. Plug in the values and calculate the energy: \[E = (28.824\:g) (0.71\:J/g°C) (25°C) = 510.9614\:J\]

Round off the answer

Round off the answer to an appropriate number of significant figures, in this case, three: Energy required = 511 J The energy required to raise the temperature of 2.4 moles of graphite by 25.0 degrees Celsius is 511 J.

Key concepts

Molar Mass

Molar mass is an essential concept in chemistry. It represents the mass of one mole of a given substance. In simple terms, it is the weight of 6.022 x 10^23 particles (atoms or molecules) of that substance. You can find molar masses on the periodic table. For example, carbon has a molar mass of 12.01 grams per mole (g/mol). This means that one mole of carbon atoms weighs 12.01 grams.

When dealing with chemical calculations, knowing the molar mass helps to convert moles, a unit for quantity, into grams, a unit for mass. Since graphite is pure carbon, its molar mass is the same as carbon, which is 12.01 g/mol. This value assists in converting between moles and grams, a critical step in many chemical calculations.

Energy Calculation

Energy calculations in chemistry often involve determining the amount of energy required to alter the temperature of a substance. The formula used is:\[E = mcΔT\]

• Here, \(E\) is the energy in Joules.
• \(m\) denotes mass in grams.
• \(c\) is the specific heat capacity in J/g°C.
• \(ΔT\) is the change in temperature in Celsius.

The specific heat capacity is a property that indicates how much energy it takes to raise the temperature of 1 gram of a substance by 1°C.

For graphite, this value is 0.71 J/g°C, which tells us relatively low energy is needed to change its temperature. When solving energy calculations, such as raising the temperature of graphite, we use the formula above by substituting the values of mass, specific heat capacity, and temperature change.

Temperature Change

Temperature change refers to the difference between the final temperature and the initial temperature of a substance. It's a straightforward concept yet vital in energy calculations. Chemically, it is represented as \(ΔT\).

For example, if we want to heat graphite from 25°C to 50°C, the temperature change \(ΔT\) would be 25°C (i.e., 50°C - 25°C). This change is what impacts the amount of energy required alongside the mass and the specific heat. The larger the temperature change, the more energy is typically needed. Thus, understanding temperature change is crucial for calculating how much energy intake is required when heating substances.

Moles to Mass Conversion

Converting moles to mass involves using the molar mass of a substance. Here's the basic principle:

• Multiply the number of moles by the molar mass of that substance.

This relationship is key when you need to determine the actual mass of a given quantity measured in moles.

For instance, if we have 2.4 moles of graphite, converting it to grams involves multiplying by the molar mass of carbon (12.01 g/mol), as all graphite is essentially carbon. \[mass = 2.4\,moles\times12.01\,g/mol = 28.824\,g\] This conversion is crucial not only for this specific calculation but also for any scientific calculations involving stoichiometry, as it allows scientists to measure and predict the outcome of chemical reactions accurately.