(a) Derive an equation to convert the specific heat of a pure substance to its molar heat capacity. (b) If you know the specific heat of aluminum, what additional information do you need to calculate the heat capacity of a particular piece of an aluminum component?

Verified step by step guidance

Step 1: Understand the relationship between specific heat and molar heat capacity. Specific heat (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius. Molar heat capacity (C_m) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius.

Step 2: Derive the equation for molar heat capacity. The molar heat capacity can be calculated using the formula:

C_m = c \times M

, where

M

is the molar mass of the substance.

Step 3: Identify the additional information needed to calculate the heat capacity of a particular piece of aluminum. You need the mass of the aluminum piece to calculate its heat capacity.

Step 4: Use the specific heat and mass to find the heat capacity. The heat capacity (C) of the aluminum piece can be calculated using the formula:

C = c \times m

, where

m

is the mass of the aluminum piece.

Step 5: Ensure you have the molar mass of aluminum. The molar mass is necessary to convert specific heat to molar heat capacity, and it is approximately 26.98 g/mol for aluminum.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a material-specific property that reflects how much energy a substance can store per unit mass. This concept is crucial for understanding how substances respond to heat and is often used in calculations involving thermal energy transfer.

Molar Heat Capacity

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. It is related to specific heat capacity through the equation C_m = c × M, where C_m is the molar heat capacity, c is the specific heat capacity, and M is the molar mass of the substance. This concept allows for the comparison of thermal properties across different substances on a per-mole basis.

Mass and Molar Mass

To calculate the heat capacity of a specific piece of aluminum, you need to know its mass. The heat capacity of an object depends not only on the material's specific heat but also on how much of that material is present. The relationship between mass and molar mass is essential for converting between specific heat and molar heat capacity, enabling accurate calculations of thermal energy changes in practical applications.

Recommended video:

Guided course

02:11

Molar Mass Concept

Related Practice

Textbook Question

Consider the decomposition of liquid benzene, C₆H₆(l), to gaseous acetylene, C₂H₂(g): C₆H₆(l) → 3 C2H₂(g) ΔH = +630 kJ (b) What is H for the formation of 1 mol of acetylene?

Textbook Question

Consider the decomposition of liquid benzene, C₆H₆(l), to gaseous acetylene, C₂H₂(g): C₆H₆(l) → 3 C2H₂(g) ΔH = +630 kJ (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction?

Textbook Question

Consider the decomposition of liquid benzene, C₆H₆(l), to gaseous acetylene, C₂H₂(g): C₆H₆(l) → 3 C2H₂(g) ΔH = +630 kJ (d) If C₆H₆(g) were consumed instead of C₆H₆(l), would you expect the magnitude of ΔH to increase, decrease, or stay the same? Explain.

Textbook Question

(b) The specific heat of aluminum is 0.9 J/(g - K). Calculate its molar heat capacity.

Textbook Question

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing 1000 g of water at 10.0 °C. Object A increases the water temperature by 3.50 °C; B increases the water temperature by 2.60 °C. (a) Which object has the larger heat capacity?

Textbook Question