A 200-gram solution of alcohol contains 180 ml of water. what is the mass percent of alcohol(remember water density)
The Correct Answer and Explanation is:
To determine the mass percent of alcohol in the solution, we first need to calculate the mass of water using its density, and then use this information to find the mass of alcohol. Finally, we’ll use the formula for mass percent to arrive at the correct answer.
Step-by-Step Solution:
- Given Information:
- Total mass of the solution: 200 grams
- Volume of water: 180 mL
- Density of water: (1 \, \text{g/mL})
- Mass of Water:
The density of water is given as (1 \, \text{g/mL}), which means 1 mL of water weighs 1 gram. Therefore, the mass of the 180 mL of water can be calculated as:
[
\text{Mass of water} = \text{Volume of water} \times \text{Density of water}
]
[
\text{Mass of water} = 180 \, \text{mL} \times 1 \, \text{g/mL} = 180 \, \text{g}
] - Mass of Alcohol:
The total mass of the solution is 200 grams, and the mass of water is 180 grams. Therefore, the mass of alcohol is:
[
\text{Mass of alcohol} = \text{Total mass of solution} – \text{Mass of water}
]
[
\text{Mass of alcohol} = 200 \, \text{g} – 180 \, \text{g} = 20 \, \text{g}
] - Mass Percent of Alcohol:
The mass percent of alcohol in the solution is calculated using the formula:
[
\text{Mass percent of alcohol} = \left(\frac{\text{Mass of alcohol}}{\text{Total mass of solution}}\right) \times 100
]
[
\text{Mass percent of alcohol} = \left(\frac{20 \, \text{g}}{200 \, \text{g}}\right) \times 100 = 10\%
]
Final Answer:
The mass percent of alcohol in the solution is 10%.
Explanation:
The mass percent of a component in a solution is a way of expressing the concentration, defined as the mass of the solute (in this case, alcohol) divided by the total mass of the solution, multiplied by 100. Here, the water’s density plays a crucial role in determining the mass of water since water is commonly used as the solvent, and its density simplifies to (1 \, \text{g/mL}) at standard conditions.
By subtracting the water’s mass from the total mass of the solution, we found the mass of alcohol. This difference gives the mass of the alcohol, allowing us to calculate the percentage concentration. This concept is essential in many chemical, biological, and industrial processes where understanding solution concentration is critical for reactions and formulations.