To solve the given problem, let's focus on the key concept of density. Density is defined as mass per unit volume:
[tex]\[ \text{Density} (\rho) = \frac{\text{Mass (m)}}{\text{Volume (V)}} \][/tex]
Below are the steps to solve the problem:
1. Understanding Density:
- Alcohol is less dense than water. This implies that for the same volume [tex]\( V \)[/tex], the density of alcohol [tex]\( \rho_{\text{alcohol}} \)[/tex] is less than the density of water [tex]\( \rho_{\text{water}} \)[/tex].
- Mathematically, [tex]\( \rho_{\text{alcohol}} < \rho_{\text{water}} \)[/tex].
2. Relating Density to Mass:
- The mass of a substance can be expressed in terms of its density and volume:
[tex]\[ \text{Mass (m)} = \text{Density} (\rho) \times \text{Volume (V)} \][/tex]
3. Comparing Masses for the Same Volume:
- Let's assume we have the same volume [tex]\( V \)[/tex] of alcohol and water.
- The mass of alcohol [tex]\( m_{\text{alcohol}} \)[/tex] would be:
[tex]\[ m_{\text{alcohol}} = \rho_{\text{alcohol}} \times V \][/tex]
- The mass of water [tex]\( m_{\text{water}} \)[/tex] would be:
[tex]\[ m_{\text{water}} = \rho_{\text{water}} \times V \][/tex]
4. Comparing the Masses:
- Since [tex]\( \rho_{\text{alcohol}} < \rho_{\text{water}} \)[/tex] and the volume [tex]\( V \)[/tex] is the same for both substances, it follows that:
[tex]\[ m_{\text{alcohol}} < m_{\text{water}} \][/tex]
Therefore, the mass of water would be greater than the mass of the same volume of alcohol. The correct choice is:
[tex]\[ \text{B. water would have a greater mass.} \][/tex]
Ensure to write your choice in the box provided for the answer in question:
B
