Question

a reaction at 7.0 °c evolves 614. mmol of dinitrogen monoxide gas. calculate the volume of dinitrogen monoxide gas that is collected. you can assume the pressure in the room is exactly 1 atm. round your answer to 3 significant digits. volume: \\(\square\\) l

Explanation:

Step1: Convert mmol to mol

We know that \( 1\space mol = 1000\space mmol \), so to convert \( 614\space mmol \) to mol, we do the following calculation:
\( n=\frac{614\space mmol}{1000\space mmol/mol}= 0.614\space mol \)

Step2: Convert temperature to Kelvin

The temperature is given as \( T = 7.0^{\circ}C \). To convert Celsius to Kelvin, we use the formula \( T(K)=T(^{\circ}C)+273.15 \).
So, \( T = 7.0 + 273.15=280.15\space K \)

Step3: Use the ideal gas law \( PV = nRT \) to find volume

The ideal gas law is \( PV = nRT \), where \( P = 1\space atm \) (given), \( n = 0.614\space mol \), \( R = 0.0821\space L\cdot atm/(mol\cdot K) \) (gas constant), and \( T = 280.15\space K \). We need to solve for \( V \), so we rearrange the formula to \( V=\frac{nRT}{P} \).
Substitute the values into the formula:
\( V=\frac{0.614\space mol\times0.0821\space L\cdot atm/(mol\cdot K)\times280.15\space K}{1\space atm} \)
First, calculate the numerator: \( 0.614\times0.0821\times280.15 \approx 0.614\times23.00 \approx 14.12 \) (approximate calculation for simplicity, more precise calculation: \( 0.614\times0.0821 = 0.0504094 \); \( 0.0504094\times280.15\approx14.12 \))
Since \( P = 1\space atm \), \( V\approx14.1\space L \) (rounded to 3 significant digits)

Answer:

\( 14.1 \)