Answered

IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

How many moles of oxygen (O₂) are contained in a 3.6 L cylinder that has a pressure of 2601 mmHg and a temperature of 31°C? Be sure your answer has the correct number of significant figures.

(Note: Reference the Fundamental constants and Conversion factors for non-SI units tables for additional information.)

Sagot :

GinnyAnsweridn
To determine the number of moles of oxygen (O₂) contained in a 3.6 L cylinder with a pressure of 2601 mmHg and a temperature of 31°C, we can use the Ideal Gas Law equation, \( PV = nRT \), where:

- \( P \) is pressure
- \( V \) is volume
- \( n \) is the number of moles
- \( R \) is the universal gas constant
- \( T \) is temperature in Kelvin

Here’s a step-by-step solution:

Step 1: Convert Temperature to Kelvin

We are given the temperature in Celsius (31°C), which we need to convert to Kelvin. The conversion formula is:

[tex]\[ T(K) = T(°C) + 273.15 \][/tex]

So,

[tex]\[ T(K) = 31 + 273.15 = 304.15 \, K \][/tex]

Step 2: Convert Pressure to atm

We are given the pressure in mmHg (2601 mmHg), which we need to convert to atmospheres (atm). The conversion factor is 1 atm = 760 mmHg. The conversion formula is:

[tex]\[ P(\text{atm}) = \frac{P(\text{mmHg})}{760} \][/tex]

So,

[tex]\[ P(\text{atm}) = \frac{2601}{760} = 3.422368421 \, atm \][/tex]

Step 3: Use the Ideal Gas Law to Solve for n (number of moles)

[tex]\[ PV = nRT \][/tex]

We can rearrange the equation to solve for \( n \):

[tex]\[ n = \frac{PV}{RT} \][/tex]

Substitute the values:

- \( P = 3.422368421 \, atm \)
- \( V = 3.6 \, L \)
- \( R = 0.0821 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}) \)
- \( T = 304.15 \, K \)

[tex]\[ n = \frac{(3.422368421 \, atm \times 3.6 \, L)}{(0.0821 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}) \times 304.15 \, K)} \][/tex]

[tex]\[ n = \frac{12.3205263156 \, \text{L} \cdot \text{atm}}{24.962215 \, \text{L} \cdot \text{atm/mole}} \][/tex]

[tex]\[ n = 0.4933990202 \, \text{moles} \][/tex]

Step 4: Round to Appropriate Significant Figures

Given the significant figures in the problem's measurements (2601 mmHg with four significant digits, 3.6 L with two significant digits, and 31°C with two significant digits), the final answer should be rounded to two significant digits.

Therefore, the number of moles of oxygen is:

[tex]\[ n ≈ 0.49 \, \text{moles} \][/tex]

So, the number of moles of oxygen (O₂) contained in the cylinder is approximately 0.49 moles.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.