Questions: How many moles of gas are contained in a human breath that occupies 0.641 L and has a pressure of 742 mmHg at 38 °C? Round your answer to 3 significant figures.

How many moles of gas are contained in a human breath that occupies 0.641 L and has a pressure of 742 mmHg at 38 °C? Round your answer to 3 significant figures.

Transcript text: How many moles of gas are contained in a human breath that occupies 0.641 L and has a pressure of $742 . \mathrm{mmHg}$ at $38 .{ }^{\circ} \mathrm{C}$ ? Round your answer to 3 significant figures. Note: Reference the Fundamental constants and Conversion factors for non-SI units table for additional information.

Solution

Solution Steps

Step 1: Convert Pressure to Atmospheres

First, we need to convert the given pressure from mmHg to atmospheres (atm). The conversion factor is: \[ 1 \, \text{atm} = 760 \, \text{mmHg} \]

Given: \[ P = 742 \, \text{mmHg} \]

Convert to atmospheres: \[ P = \frac{742 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 0.9763 \, \text{atm} \]

Step 2: Convert Temperature to Kelvin

Next, we convert the given temperature from Celsius to Kelvin. The conversion formula is: \[ T(K) = T(^{\circ}C) + 273.15 \]

Given: \[ T = 38 \, ^{\circ}\text{C} \]

Convert to Kelvin: \[ T = 38 + 273.15 = 311.15 \, \text{K} \]

Step 3: Use the Ideal Gas Law to Find Moles

We use the Ideal Gas Law, which is: \[ PV = nRT \]

Where:

$ P $ is the pressure in atm
$ V $ is the volume in liters
$ n $ is the number of moles
$ R $ is the ideal gas constant, $ R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} $
$ T $ is the temperature in Kelvin

Rearrange the equation to solve for $ n $: \[ n = \frac{PV}{RT} \]

Substitute the known values: \[ n = \frac{(0.9763 \, \text{atm})(0.641 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(311.15 \, \text{K})} \]

Step 4: Calculate the Number of Moles

Perform the calculation: \[ n = \frac{0.6258}{25.5442} = 0.02450 \, \text{mol} \]