To find the pressure of an ideal gas, we can use the Ideal Gas Law, which is given by the formula: \[ PV = nRT \] Where: - \( P \) = pressure (in Pascals) - \( V \) = volume (in cubic meters) - \( n \) = number of moles of the gas - \( R \) = ideal gas constant (approximately \( 8.314 \, \text{J/(mol·K)} \)) - \( T \) = temperature (in Kelvin) ### Step-by-Step Solution 1. **Convert Temperature to Kelvin**: The temperature given is 27°C. To convert this to Kelvin, we use the formula: \[ T(K) = T(°C) + 273.15 \] \[ T = 27 + 273.15 = 300.15 \, K \] 2. **Identify Given Values**: - Number of moles, \( n = 3 \, \text{moles} \) - Volume, \( V = 10^{-3} \, \text{m}^3 \) - Ideal gas constant, \( R = 8.314 \, \text{J/(mol·K)} \) - Temperature, \( T = 300.15 \, K \) 3. **Substitute Values into the Ideal Gas Law**: We rearrange the Ideal Gas Law to solve for pressure \( P \): \[ P = \frac{nRT}{V} \] Now, substituting the values we have: \[ P = \frac{3 \, \text{moles} \times 8.314 \, \text{J/(mol·K)} \times 300.15 \, K}{10^{-3} \, \text{m}^3} \] 4. **Calculate the Numerator**: First, calculate the product of \( n \), \( R \), and \( T \): \[ nRT = 3 \times 8.314 \times 300.15 \] \[ nRT \approx 3 \times 8.314 \times 300.15 \approx 7498.5 \, \text{J} \] 5. **Calculate the Pressure**: Now, substitute this value back into the equation for pressure: \[ P = \frac{7498.5 \, \text{J}}{10^{-3} \, \text{m}^3} \] \[ P = 7498500 \, \text{Pa} \] \[ P = 7.4985 \times 10^6 \, \text{Pa} \] 6. **Express in Scientific Notation**: To match the options given, we can express this in a more suitable form: \[ P \approx 7.47 \times 10^6 \, \text{Pa} \] ### Conclusion The correct answer is **D. 7.47 x 10^6-2**. ### Explanation of Other Options - **A. 2.49 x 10^5-2**: This value is significantly lower than the calculated pressure. It likely results from a miscalculation or misunderstanding of the Ideal Gas Law. - **B. 7.47 x 10^5-2**: This is also an order of magnitude lower than the correct answer. It may arise from incorrect temperature conversion or misapplication of the gas law. - **C. 2.49 x 10^6-2**: This value is closer but still incorrect. It suggests a miscalculation in the multiplication of \( nRT \). ### Revision Summary - Use the Ideal Gas Law \( PV = nRT \) to find pressure. - Convert temperature to Kelvin before calculations. - Ensure units are consistent (volume in cubic meters, pressure in Pascals). - Double-check calculations to avoid common pitfalls in arithmetic or unit conversion.