A sample of an unknown compound is vaporized at 

140.°C

. The gas produced has a volume of 

2100.mL

 at a pressure of 

1.00atm

, and it weighs 

1.99g

.

Assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. Be sure your answer has the correct number of significant digits.

To find the molar mass (\( M \)) of the compound, we can use the Ideal Gas Law:

\[
PV = nRT
\]

where:
- \( P \) = pressure of the gas (1.00 atm),
- \( V \) = volume of the gas (2,100 mL = 2.1 L),
- \( n \) = number of moles of the gas,
- \( R \) = ideal gas constant (0.0821 L·atm / K·mol),
- \( T \) = temperature in Kelvin (140°C + 273.15 = 413.15 K).

1. **Calculate the moles of gas (\( n \)):**

   Rearrange the Ideal Gas Law to solve for \( n \):
   \[
   n = \frac{PV}{RT}
   \]

   Substitute the values:
   \[
   n = \frac{(1.00 \, \text{atm})(2.1 \, \text{L})}{(0.0821 \, \text{L·atm / K·mol})(413.15 \, \text{K})}
   \]

   Calculate \( n \):
   \[
   n \approx \frac{2.1}{33.916215} \approx 0.0619 \, \text{moles}
   \]

2. **Calculate the molar mass (\( M \)):**

   Molar mass (\( M \)) is defined as the mass of the compound divided by the number of moles:
   \[
   M = \frac{\text{mass}}{n}
   \]

   Substitute the values:
   \[
   M = \frac{1.99 \, \text{g}}{0.0619 \, \text{moles}}
   \]

   Calculate \( M \):
   \[
   M \approx 32.1 \, \text{g/mol}
   \]

**Answer:** The molar mass of the compound is approximately \( 32.1 \, \text{g/mol} \), rounded to three significant figures.

Would you like more details on any part of this calculation? 

---

Here are some related questions to explore:

1. How would changing the temperature affect the calculated molar mass?
2. What assumptions do we make when using the Ideal Gas Law for real gases?
3. How do significant figures impact the accuracy of scientific calculations?
4. What are the consequences if the gas does not behave ideally under these conditions?
5. How does the choice of units for pressure and volume affect the Ideal Gas Law calculation?

**Tip:** Always convert temperatures to Kelvin when using the Ideal Gas Law; the formula requires absolute temperature to ensure accuracy.

A sample of an unknown compound is vaporized at 140°C. The gas produced has a volume of 2100 mL at a pressure of 1.00 atm, and it weighs 1.99 g. Assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. Be sure your answer has the correct number of significant digits.

Learn how to calculate the molar mass of an unknown compound by applying the Ideal Gas Law, given the conditions of temperature, pressure, and mass. This solution includes detailed steps for converting units, applying the gas law formula, and ensuring significant figures are correctly maintained. Suitable for high school chemistry students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation