Answer: 14.6 L
Explanation:
To find the volume of CO₂ exhaled by a person, we can use the ideal gas law, which is given by:
\($PV = nRT\)
where:
\($P$\) is the pressure of the gas (in atmospheres, atm)
\($V$\) is the volume of the gas (in liters, L)
\($n$\) is the number of moles of the gas
\($R$\) is the ideal gas constant (0.0821 L·atm/mol·K)
\($T$\) is the temperature of the gas (in Kelvin, K)
First, we need to convert the mass of CO₂ to moles. The molar mass of CO₂ (carbon dioxide) is approximately 44.01 g/mol. Given the mass of CO₂ exhaled is 25.5 g, the number of moles, n, can be calculated as:
\($n = \frac{m}{\text{molar mass}} = \frac{25.5 , \text{g}}{44.01 , \text{g/mol}} = 0.58 , \text{mol}$\)
The temperature given is 36.9°C. To convert this to Kelvin:
\($T = 36.9^\circ \text{C} + 273.15 = 310.05 , \text{K}$\)
Now, substituting the values into the ideal gas law:
\($PV = nRT\)
We rearrange to solve for \($V\):
\($V = \frac{nRT}{P}\)
\($V = \frac{\left(\frac{25.5 , \text{g}}{44.01 , \text{g/mol}}\right) \times 0.0821 , \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}} \times 310.05 , \text{K}}{1.01 , \text{atm}}\)
\($V = 14.6 L $\) (rounded to three significant figures)
