Question

what volume does 4.53 moles of hydrogen at 1.78 atm and 301 k occupy? ? l

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 gas constant, and \( T \) is temperature. We need to solve for \( V \), so we rearrange the formula to \( V=\frac{nRT}{P} \).

Step2: Identify the values

We know:

• \( n = 4.53 \) moles
• \( P = 1.78 \) atm
• \( T = 301 \) K
• \( R = 0.0821 \frac{L\cdot atm}{mol\cdot K} \) (gas constant for these units)

Step3: Substitute the values into the formula

Substitute \( n \), \( R \), \( T \), and \( P \) into \( V=\frac{nRT}{P} \):

$$ V=\frac{4.53\ mol\times0.0821\frac{L\cdot atm}{mol\cdot K}\times301\ K}{1.78\ atm} $$

Step4: Calculate the numerator first

Calculate \( 4.53\times0.0821\times301 \):
\( 4.53\times0.0821 = 0.371913 \)
\( 0.371913\times301 = 111.945813 \)

Step5: Divide by the pressure

Now divide the numerator by \( P = 1.78 \) atm:
\( V=\frac{111.945813}{1.78}\approx62.89 \)

Answer:

\( 62.9 \) (rounded to three significant figures, or depending on precision requirements, the value is approximately \( 62.9 \) L)