Question

dinitrogen monoxide gas is collected at -12.0 °c in an evacuated flask with a measured volume of 5.0 l. when all the gas has been collected, the pressure in the flask is measured to be 0.240 atm. calculate the mass and number of moles of dinitrogen monoxide gas that were collected. round your answer to 2 significant digits. mass: g mole: mol

Explanation:

Step1: Convert temperature to Kelvin

The temperature is given as \(-12.0^\circ \text{C}\). To convert to Kelvin, we use the formula \(T(K) = T(^\circ \text{C}) + 273.15\). So, \(T = -12.0 + 273.15 = 261.15 \text{ K}\).

Step2: Use the ideal gas law to find moles

The ideal gas law is \(PV = nRT\), where \(P = 0.240 \text{ atm}\), \(V = 5.0 \text{ L}\), \(R = 0.0821 \text{ L·atm/(mol·K)}\), and \(T = 261.15 \text{ K}\). We solve for \(n\):
\[
n = \frac{PV}{RT}
\]
Substituting the values:
\[
n = \frac{0.240 \text{ atm} \times 5.0 \text{ L}}{0.0821 \text{ L·atm/(mol·K)} \times 261.15 \text{ K}}
\]
First, calculate the numerator: \(0.240 \times 5.0 = 1.2\)
Then, calculate the denominator: \(0.0821 \times 261.15 \approx 21.44\)
So, \(n = \frac{1.2}{21.44} \approx 0.056 \text{ mol}\) (rounded to 2 significant digits)

Step3: Calculate the molar mass of \( \text{NO} \)

The molar mass of \( \text{N} \) is \(14.01 \text{ g/mol}\) and \( \text{O} \) is \(16.00 \text{ g/mol}\). So, molar mass of \( \text{NO} = 14.01 + 16.00 = 30.01 \text{ g/mol}\)

Step4: Calculate the mass

Using the formula \( \text{mass} = n \times \text{molar mass} \), we have:
\[
\text{mass} = 0.056 \text{ mol} \times 30.01 \text{ g/mol} \approx 1.7 \text{ g}
\] (rounded to 2 significant digits)

Answer:

mole: \(0.056 \text{ mol}\)
mass: \(1.7 \text{ g}\)