Question

question 28 of 30 how many moles of neon (ne) gas have a volume of 0.84 l and a pressure of 4.6 atm at 222 k? (the universal gas constant is 0.0821 l·atm/mol·k.) a. 4.7 mol b. 70. mol c. 0.010 mol d. 0.21 mol

Explanation:

Step1: Recall the Ideal Gas Law

The Ideal Gas Law is given by \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is temperature in Kelvin. We need to solve for \( n \), so we rearrange the formula to \( n=\frac{PV}{RT} \).

Step2: Identify the given values

We are given:

• \( P = 4.6 \, \text{atm} \)
• \( V = 0.84 \, \text{L} \)
• \( R = 0.0821 \, \text{L·atm/mol·K} \)
• \( T = 222 \, \text{K} \)

Step3: Substitute the values into the formula

Substitute the values into \( n=\frac{PV}{RT} \):
\[
n = \frac{(4.6 \, \text{atm})(0.84 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K})(222 \, \text{K})}
\]

Step4: Calculate the numerator and the denominator

First, calculate the numerator: \( (4.6)(0.84) = 3.864 \)
Then, calculate the denominator: \( (0.0821)(222) \approx 18.2262 \)

Step5: Divide the numerator by the denominator

Now, divide the numerator by the denominator: \( n=\frac{3.864}{18.2262} \approx 0.212 \, \text{mol} \), which is approximately \( 0.21 \, \text{mol} \).

Answer:

D. 0.21 mol