How much heat must be added to 50.0 g of solid sodium, Na, at 25.0^∘ C to give the liquid at it

How much heat must be added to 50.0 g of solid sodium, Na,...

How much heat must be added to $50.0 \mathrm{~g}$ of solid sodium, $\mathrm{Na},$ at $25.0^{\circ} \mathrm{C}$ to give the liquid at its melting point, $97.8^{\circ} \mathrm{C} ?$ The heat capacity of solid sodium is $28.2 \mathrm{~J} /$ $(\mathrm{K} \cdot \mathrm{mol}),$ and its heat of fusion is $2.60 \mathrm{~kJ} / \mathrm{mol}$

Key Concepts

Molar Heat Capacity

Molar heat capacity is the amount of energy required to raise the temperature of one mole of a substance by one degree Kelvin. This concept is fundamental when calculating the energy needed for sensible heat—that is, the increase in temperature before a phase change occurs—in thermodynamic processes.

Heat of Fusion

Heat of fusion is the amount of energy required to change one mole of a substance from its solid phase to its liquid phase at its melting point without a change in temperature. It is a key concept when dealing with phase transitions that involve breaking intermolecular bonds during melting.

Conversion from Mass to Moles

The conversion from mass to moles involves using the molar mass of a substance to translate the mass given in grams to the equivalent number of moles. This conversion is essential for applying thermodynamic constants, such as molar heat capacity or heat of fusion, which are defined on a per-mole basis.

Energy Calculations in Calorimetry

Calorimetry involves measuring or calculating the amount of heat exchanged during physical and chemical processes. In problems like this, the total heat required is computed by summing the heat needed for raising the temperature (using molar heat capacity) and the heat necessary for the phase change (using heat of fusion), thereby illustrating the application of energy conservation in a thermodynamic system.

Transcript

00:01 Okay, so this question is a little bit complicated because it involves multiple processes.

00:09 So you have actually calculated the energy involves in each process.

00:14 So it says how much heat must be added to 50 grams of sodium, solid sodium, to give the liquid at its melting point at 97 .8.

00:27 So, reading this question, we know the two processes happened.

00:34 Initially, we have the solid sodium, which is at 25 degrees c.

00:44 And then you increase the temperature to its melting point, right? but still, it's a solid, but it's at the melting point, 97 .8 degree c.

01:00 And at this point, you melt the solid sodium.

01:09 So then it becomes a liquid sodium.

01:14 But still, the temperature is 97 .8 degrees c.

01:19 So you can see, it actually involves two processes.

01:23 One is just simply increased the temperature, and the energy involved is related to the heat capacity.

01:31 And the second step is actually the melting process, which relates to the heat of the fueling during the process.

01:43 So what we need to do is just calculate the energy involved for each step.

01:50 So for the first step, when the solid sodium goes from 25 degrees c to the 97 .80, what is the energy we need to provide? so we know this step, the energy we need to provide actually equals to the heat capacity times the times, so in this question you can see the heat capacity given is kelvin per more, is more.

02:31 So here it's a more heat capacity.

02:34 So here we times the more of the sodium.

02:38 So before that, we can first calculate the mores of the sodium, which equals to the mass over the more mass, which is 50 grams over 23 grams per more, which actually equals to around 2 .174 more.

03:07 So now we can just plug in number to calculate the q1...

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