Under which of the following conditions would the same amount by mass of sugar diffuse the fastsest?

300 ml ice tea with sugar cube

300 ml ice tea with table sugar

300 ml hot tea and a sugar cube

300 ml hot tea and table sugar

The rate of diffusion of a substance is influenced by several factors, including temperature, concentration gradient, and the nature of the medium in which diffusion takes place. Based on these factors, the condition under which the same amount by mass of sugar would diffuse the fastest is when the sugar is added to hot tea.

In this scenario, the hot tea has a higher temperature compared to the ice tea, which increases the kinetic energy of the sugar molecules. Higher kinetic energy leads to increased movement and collisions among the sugar molecules, facilitating faster diffusion. Additionally, the temperature difference between the sugar and the hot tea creates a steeper concentration gradient, promoting faster diffusion.

Therefore, in the given options, pouring sugar into 300 ml of hot tea would result in the fastest diffusion of the same amount by mass of sugar.

To determine under which conditions the same amount of sugar would diffuse the fastest, we need to consider the factors that affect the rate of diffusion. The rate of diffusion is influenced by temperature, concentration gradient, and molecular weight.

In the given options, let's analyze each scenario:

1. 300 ml of ice tea with a sugar cube:
In this case, the tea is cold, and the sugar cube is dense. Since temperature affects diffusion, the low temperature of the ice tea would slow down the diffusion process. Also, the sugar cube has a larger molecular weight compared to granulated sugar, which means it may diffuse more slowly. Therefore, this option is likely to have a slower diffusion rate.

2. 300 ml of ice tea with table sugar:
Similar to the previous scenario, the ice tea is cold, but this time we are using table sugar instead of a sugar cube. Table sugar generally has a smaller molecular weight than a sugar cube, which could enhance the diffusion rate. However, considering the low temperature of the ice tea, the rate of diffusion would still be slower compared to a higher temperature scenario. Therefore, the diffusion rate in this option may be slower as well.

3. 300 ml of hot tea and a sugar cube:
Now, the tea is hot in this scenario. The higher temperature increases the kinetic energy of the particles, making them move faster and increasing the rate of diffusion. However, the sugar cube's larger molecular weight may still hinder the diffusion to some extent. Nonetheless, the higher temperature overall may result in a faster diffusion rate compared to the cold tea scenarios.

4. 300 ml of hot tea and table sugar:
This scenario combines a higher temperature (which increases the rate of diffusion) with the use of table sugar (which has a smaller molecular weight). Both factors work together to enhance the diffusion rate. Therefore, this option is likely to have the fastest diffusion rate among the given choices.

In conclusion, out of the given options, 300 ml of hot tea with table sugar would have the fastest diffusion rate, as the combination of higher temperature and smaller molecular weight would facilitate the diffusion process.