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The maximum amount of potassium chloride, [tex]\(A\)[/tex], in grams [tex]\((g)\)[/tex], which can be dissolved in 100 g of water at [tex]\(C\)[/tex] degrees Celsius is given by the equation:

[tex]\[ A = 27 + 0.3C \][/tex]

Which of the following is the best interpretation of 0.3 as shown in the given equation?

A. The amount of potassium chloride (in grams) that can be dissolved increases by 0.3 g for each degree Celsius increase in temperature.

B. 0.3 g of potassium chloride can be dissolved at 0 degrees Celsius.

C. The amount of water required to dissolve potassium chloride decreases by 0.3 g for each degree Celsius increase in temperature.

D. The amount of potassium chloride (in grams) that can be dissolved decreases by 0.3 g for each degree Celsius increase in temperature.

Sagot :

GinnyAnsweridn
Let's examine the given equation for the maximum amount of potassium chloride, [tex]\( A \)[/tex], that can be dissolved in 100 grams of water at [tex]\( C \)[/tex] degrees Celsius. The equation is:

[tex]\[ A = 27 + 0.3C \][/tex]

In this equation:
- [tex]\( A \)[/tex] represents the maximum amount of potassium chloride in grams that can dissolve in 100 grams of water.
- [tex]\( C \)[/tex] represents the temperature in degrees Celsius.

The equation can be understood as follows:
- The term [tex]\( 27 \)[/tex] is a constant that shows the base amount of potassium chloride that can dissolve at [tex]\( 0 \)[/tex] degrees Celsius.
- The term [tex]\( 0.3C \)[/tex] shows how the solubility of potassium chloride changes with temperature.

Now let's focus on the specific coefficient [tex]\( 0.3 \)[/tex] in the equation [tex]\( 27 + 0.3C \)[/tex]:

### Step-by-Step Interpretation of [tex]\( 0.3 \)[/tex]:

1. Coefficient Analysis:
- The coefficient [tex]\( 0.3 \)[/tex] is associated with the variable [tex]\( C \)[/tex], which represents the temperature.

2. Impact on Solubility:
- The coefficient [tex]\( 0.3 \)[/tex] indicates how the maximum amount of potassium chloride that can be dissolved changes with respect to temperature. Specifically, for each 1 degree Celsius increase in temperature, the [tex]\( 0.3C \)[/tex] term shows an increase in the grams of potassium chloride that can dissolve.

3. Measurement of Increase:
- A coefficient of [tex]\( 0.3 \)[/tex] means that for every degree Celsius increase in temperature, the solubility of potassium chloride in 100 grams of water increases by [tex]\( 0.3 \)[/tex] grams.

### Conclusion:
The best interpretation of [tex]\( 0.3 \)[/tex] as shown in the given equation is:
- For each 1 degree Celsius increase in temperature, the amount of potassium chloride that can be dissolved in 100 grams of water increases by [tex]\( 0.3 \)[/tex] grams.

This interpretation directly explains how the solubility of potassium chloride is influenced by changes in temperature according to the given equation.
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