Titanium metal is used as a structural material in many high-tech applications, such as in jet engines. what is the specific heat of titanium in J/(g·°C) if it takes 89.7 J to raise the temeprature of a 33.0 g block of 5.20 °C? What is the molar heat capacity of titanium J/(mol·°C)?

Verified step by step guidance

1. Identify the given values: heat energy (Q) = 89.7 J, mass (m) = 33.0 g, and temperature change (ΔT) = 5.20 °C.
2. Use the formula for specific heat capacity (c), which is c = Q / (m * ΔT). Plug in the values to find the specific heat of titanium.
3. To find the molar heat capacity, first determine the molar mass of titanium. Titanium (Ti) has an atomic mass of approximately 47.87 g/mol.
4. Calculate the number of moles of titanium in the 33.0 g block using the formula: moles = mass / molar mass.
5. Use the formula for molar heat capacity (C), which is C = Q / (moles * ΔT). Calculate the molar heat capacity using the values obtained from the previous steps.

Key Concepts

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 crucial property that helps in understanding how substances respond to heat. The formula to calculate specific heat (c) is c = q / (m × ΔT), where q is the heat added, m is the mass, and ΔT is the change in temperature.

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 but is expressed per mole rather than per gram. The relationship between specific heat and molar heat capacity can be established using the molar mass of the substance, allowing for conversions between the two.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In the context of the question, it involves calculating how much energy is needed to change the temperature of titanium. Understanding heat transfer is essential for applying the concepts of specific and molar heat capacities in practical scenarios.