Questions: A geochemist in the field takes a 18.0 mL sample of water from a rock pool lined with crystals of a certain mineral compound X. He notes the temperature of the pool, 20 °C, and caps the sample carefully. Back in the lab, the geochemist filters the sample and then evaporates all the water under vacuum. Crystals of X are left behind. The researcher washes, dries and weighs the crystals. They weigh 1.4 g. Using only the information above, can you calculate the solubility of X in water at 20 °C? Yes If you said yes, calculate it. Be sure your answer has a unit symbol and the right number of significant digits.

A geochemist in the field takes a 18.0 mL sample of water from a rock pool lined with crystals of a certain mineral compound X. He notes the temperature of the pool, 20 °C, and caps the sample carefully. Back in the lab, the geochemist filters the sample and then evaporates all the water under vacuum. Crystals of X are left behind. The researcher washes, dries and weighs the crystals. They weigh 1.4 g. Using only the information above, can you calculate the solubility of X in water at 20 °C? Yes If you said yes, calculate it. Be sure your answer has a unit symbol and the right number of significant digits.
Transcript text: A geochemist in the field takes a 18.0 mL sample of water from a rock pool lined with crystals of a certain mineral compound $X$. He notes the temperature of the pool, $20 .{ }^{\circ} \mathrm{C}$, and caps the sample carefully. Back in the lab, the geochemist filters the sample and then evaporates all the water under vacuum. Crystals of $X$ are left behind. The researcher washes, dries and weighs the crystals. They weigh 1.4 g . Using only the information above, can you calculate the solubility of $X$ in water at $20 .{ }^{\circ} \mathrm{C}$ ? Yes If you said yes, calculate it. Be sure your answer has a unit symbol and the right number of significant digits.
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Solution

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Solution Steps

Step 1: Determine the mass of the solute

The mass of the solute \(X\) left behind after evaporating the water is given as 1.4 g.

Step 2: Determine the volume of the solvent

The volume of the water sample taken is 18.0 mL.

Step 3: Calculate the solubility

Solubility is defined as the amount of solute that can dissolve in a given amount of solvent at a specific temperature. It is usually expressed in grams of solute per liter of solvent (g/L).

First, convert the volume of water from mL to L: \[ 18.0 \, \text{mL} = 0.0180 \, \text{L} \]

Next, calculate the solubility \(S\) using the formula: \[ S = \frac{\text{mass of solute}}{\text{volume of solvent}} \] \[ S = \frac{1.4 \, \text{g}}{0.0180 \, \text{L}} \] \[ S = 77.7778 \, \text{g/L} \]

Step 4: Round to the correct number of significant digits

The given data (1.4 g and 18.0 mL) both have 2 significant digits. Therefore, the solubility should also be reported with 2 significant digits: \[ S = 78 \, \text{g/L} \]

Final Answer

\[ \boxed{S = 78 \, \text{g/L}} \]

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