Final answer:
The number of moles of gas in a human breath at 0.65 L, 756 mm Hg, and 36°C can be calculated using the Ideal Gas Law, converting the temperature to Kelvin and the pressure to atmospheres, and then using the gas constant R.
Step-by-step explanation:
To determine the number of moles of gas in a human breath that occupies 0.65 L, has a pressure of 756 mm Hg at 36°C, we must use the Ideal Gas Law which is PV = nRT. Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. First, convert the provided temperature to Kelvin by adding 273.15 to the Celsius temperature: 36 + 273.15 = 309.15 K. Next, convert the pressure from mm Hg to atmospheres since the gas constant R value commonly used is in terms of L·atm/(mol·K). 756 mm Hg is converted to ≈ 0.994 atm (1 atm = 760 mm Hg). Now use the value of R = 0.0821 L·atm/(mol·K) and rearrange the Ideal Gas Law to solve for n: n = (PV) / (RT). Substituting the values: n = (0.994 atm × 0.65 L) / (0.0821 L·atm/(mol·K) × 309.15 K).
After performing the calculation, we obtain the number of moles of gas contained in a human breath under the given conditions.