Questions: A chemistry student needs 40.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is 0.706 g·cm^-3. Calculate the volume of diethylamine the student should pour out: Round your answer to 3 significant digits.

A chemistry student needs 40.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is 0.706 g·cm^-3. Calculate the volume of diethylamine the student should pour out: Round your answer to 3 significant digits.
Transcript text: A chemistry student needs 40.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is $0.706 \mathrm{~g}^{\cdot} \mathrm{cm}^{-3}$. Calculate the volume of diethylamine the student should pour out: Round your answer to 3 significant digits.
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Solution

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Solution Steps

Step 1: Identify the given values

The problem provides the following information:

  • Mass of diethylamine, \( m = 40.0 \) g
  • Density of diethylamine, \( \rho = 0.706 \) g/cm\(^3\)
Step 2: Use the density formula to find the volume

The formula for density is: \[ \rho = \frac{m}{V} \] where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume. We need to solve for \( V \): \[ V = \frac{m}{\rho} \]

Step 3: Substitute the given values into the formula

Substitute \( m = 40.0 \) g and \( \rho = 0.706 \) g/cm\(^3\) into the formula: \[ V = \frac{40.0 \, \text{g}}{0.706 \, \text{g/cm}^3} \]

Step 4: Calculate the volume

Perform the division: \[ V = \frac{40.0}{0.706} \approx 56.6532 \, \text{cm}^3 \]

Step 5: Round the answer to 3 significant digits

Round \( 56.6532 \) cm\(^3\) to 3 significant digits: \[ V \approx 56.7 \, \text{cm}^3 \]

Final Answer

\[ \boxed{V = 56.7 \, \text{cm}^3} \]

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