Alright, let's solve this step-by-step.
1. Understand the Question:
We need to determine how much energy is released when 10.6 grams of steam condenses into water. The heat of vaporization of water is given as 2,257 joules/gram.
2. Given Values:
- Mass of steam, [tex]\( m \)[/tex] = 10.6 grams
- Heat of vaporization, [tex]\( L_v \)[/tex] = 2,257 joules/gram
3. Formula to Use:
The amount of energy [tex]\( Q \)[/tex] released when steam condenses is given by the formula:
[tex]\[
Q = m \times L_v
\][/tex]
where:
- [tex]\( Q \)[/tex] = Energy released (in joules)
- [tex]\( m \)[/tex] = Mass of the steam (in grams)
- [tex]\( L_v \)[/tex] = Heat of vaporization (in joules/gram)
4. Calculation:
Substitute the given values into the formula:
[tex]\[
Q = 10.6 \text{ grams} \times 2,257 \text{ joules/gram}
\][/tex]
5. Perform the Multiplication:
[tex]\[
Q = 10.6 \times 2,257
\][/tex]
After multiplying, we obtain:
[tex]\[
Q = 23,924.2 \text{ joules}
\][/tex]
6. Significant Figures:
Both the mass (10.6 grams) and the heat of vaporization (2,257 joules/gram) are given to three significant figures. Thus, the final answer should also be expressed to three significant figures.
The amount of energy released from the water is [tex]\( \boxed{23924.2} \)[/tex] joules.
