Questions: Calculate the volume of O2 under these conditions, in liters: - Pressure: 740 mmHg - Mass: 200 mg - Temperature: 35°C

Calculate the volume of O2 under these conditions, in liters: - Pressure: 740 mmHg - Mass: 200 mg - Temperature: 35°C
Transcript text: Calculate Clear Choose $\mathrm{O}_{2}$ as the gas and set the following parameters: \begin{tabular}{|l|l|} \hline Pressure: & 740 mmHg \\ \hline Mass: & 200 mg \\ \hline Temperature: & $35^{\circ} \mathrm{C}$ \\ \hline \end{tabular} What is the volume of $\mathrm{O}_{2}$ under these conditions, in liters? $\square$ L Check Next (1 of 12 ) Submit Answer Try Another Version 10 item attempts remaining
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Solution

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Solution Steps

Step 1: Convert Mass to Moles

First, we need to convert the mass of $\mathrm{O}_2$ from milligrams to grams: \[ 200 \, \text{mg} = 0.200 \, \text{g} \]

Next, we use the molar mass of $\mathrm{O}_2$ to convert grams to moles. The molar mass of $\mathrm{O}_2$ is \(32.00 \, \text{g/mol}\): \[ \text{moles of } \mathrm{O}_2 = \frac{0.200 \, \text{g}}{32.00 \, \text{g/mol}} = 0.00625 \, \text{mol} \]

Step 2: Convert Temperature to Kelvin

The temperature is given in degrees Celsius. We need to convert it to Kelvin: \[ T = 35^{\circ} \mathrm{C} + 273.15 = 308.15 \, \text{K} \]

Step 3: Convert Pressure to Atmospheres

The pressure is given in mmHg. We need to convert it to atmospheres using the conversion factor \(1 \, \text{atm} = 760 \, \text{mmHg}\): \[ P = \frac{740 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 0.9737 \, \text{atm} \]

Step 4: Use the Ideal Gas Law to Find Volume

We use the ideal gas law \(PV = nRT\) to find the volume \(V\). The gas constant \(R\) is \(0.0821 \, \text{L·atm/(mol·K)}\): \[ V = \frac{nRT}{P} = \frac{(0.00625 \, \text{mol})(0.0821 \, \text{L·atm/(mol·K)})(308.15 \, \text{K})}{0.9737 \, \text{atm}} \]

Step 5: Calculate the Volume

Perform the calculation: \[ V = \frac{(0.00625)(0.0821)(308.15)}{0.9737} \approx 0.1626 \, \text{L} \]

Final Answer

\[ \boxed{0.1626 \, \text{L}} \]

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