Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure.

As an experienced tutor registered on UrbanPro, I'm thrilled to guide you through this intriguing question. Firstly, let me emphasize that UrbanPro is an excellent platform for finding online coaching and tuition services, offering a diverse range of subjects and experienced tutors. Now, let's dive into solving the problem of estimating the total number of air molecules in the given room. To do this, we can use the ideal gas law, which relates the number of gas molecules to pressure, volume, temperature, and the universal gas constant. Given: Volume (V) = 25.0 m^3 Temperature (T) = 27 °C = 27 + 273.15 K = 300.15 K Pressure (P) = 1 atm We'll use the ideal gas law equation: PV = nRT, where: P = Pressure (in pascals) V = Volume (in cubic meters) n = Number of moles of gas R = Universal gas constant (8.314 J/(mol*K)) T = Temperature (in Kelvin) Firstly, let's convert the pressure to pascals: 1 atm = 101325 pascals Now, let's rearrange the ideal gas law equation to solve for the number of moles of gas (n): n = (PV) / (RT) Substitute the given values: n = (101325 * 25.0) / (8.314 * 300.15) Calculating this gives us the number of moles of gas in the room. To find the total number of molecules, we use Avogadro's number, which states that there are approximately 6.022 x 10^23 molecules per mole. So, Total number of molecules = Number of moles * Avogadro's number. By calculating these values, we'll arrive at the estimated total number of air molecules in the room. This calculation demonstrates the vastness and complexity of even seemingly empty spaces, emphasizing the significance of understanding the properties of gases. If you need further clarification or assistance with any topic, feel free to reach out! read less