Problem 4 - General Chemistry

Question

Explain why \(15 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) melts more ice than \(15 \mathrm{~g}\) of liquid water at \(100^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

Steam at 100°C releases more heat (40170 J) than water at 100°C (6270 J), thus melting more ice.

Step 1: Determine the heat released by steam

First, calculate the heat released when 15 g of steam at 100°C condenses into water at 100°C. The heat of vaporization of water is approximately 2260 J/g. The formula is given by \( Q = mL \), where \( m \) is the mass and \( L \) is the heat of vaporization. \( Q = 15 \text{ g} \times 2260 \text{ J/g} = 33900 \text{ J} \).

Step 2: Calculate the heat released when steam cools to 0°C

After condensing, the water from steam must cool to 0°C. Using the formula \( Q = mc\Delta T \), where \( c \) is the specific heat capacity of water (4.18 J/g°C) and \( \Delta T = 100°C \), the heat is \( Q = 15 \text{ g} \times 4.18 \text{ J/g°C} \times 100°C = 6270 \text{ J} \).

Step 3: Total heat released by steam

Add the heat released from condensation and cooling together: \( 33900 \text{ J} + 6270 \text{ J} = 40170 \text{ J} \).

Step 4: Calculate the heat released by liquid water

Water at 100°C only needs to cool to 0°C, using the same formula as above, \( Q = 15 \text{ g} \times 4.18 \text{ J/g°C} \times 100°C = 6270 \text{ J} \).

Step 5: Comparison of heat released

The total heat released by steam (40170 J) is much greater than that released by equivalent hot water (6270 J). Therefore, steam melts more ice, due to both the latent heat of vaporization and subsequent cooling.

Key Concepts

Latent Heat of Vaporization

When a substance changes from a liquid to a gas, it requires additional energy known as the latent heat of vaporization. This energy is necessary for overcoming the intermolecular forces in a liquid to transform it into a gaseous state. In our steam example, the latent heat of vaporization for water is approximately 2260 J/g. This means that to convert 1 gram of water at 100°C into steam at the same temperature, 2260 joules of energy are needed.

In practical terms:

• For 15 grams of steam, the energy associated with this phase change is significant, amounting to 33,900 joules.
• This energy is released when the steam condenses back into liquid water.

The large amount of heat released during condensation is why steam can transfer more energy than hot water, enabling it to melt more ice when it cools down.

Specific Heat Capacity

Specific heat capacity is a property of materials that describes how much heat is required to change the temperature of a certain mass by 1°C. For water, the specific heat capacity is 4.18 J/g°C. This property plays a critical role in the cooling of water.

An example statement:

• When 15 grams of water cools from 100°C to 0°C, it releases energy calculated as: 15 g × 4.18 J/g°C × 100°C = 6,270 joules.

This calculation applies to both 15 grams of steam once condensed into water, and to 15 grams of hot water. This shared property underscores why cooling alone contributes less energy than the initial phase change from steam to water.

Phase Change Cooling

Phase change cooling refers to the process where a substance releases or absorbs heat during a change in its state (phase) without a temperature change. In the case of steam, two major processes occur:

• Condensation: Steam releases latent heat as it turns into water, delivering significant heat energy.
• Cooling of Condensed Water: Subsequent cooling of this water releases additional energy as it cools from 100°C to 0°C.

The combination of these processes tremendously increases the total energy transferred by the steam compared to an equivalent mass of liquid water. The total energy released by steam is thus much greater due to both its latent heat of vaporization and its specific heat capacity during cooling.