20. A \( 350.0 \mathrm{~cm}^{3} \) sample of helium gas is collected at \( 22.0^{\circ} \mathrm{C} \) and 99.3 kP . What volune wald this gas sooser at STP?

To find the volume of the helium gas at Standard Temperature and Pressure (STP), we can use the ideal gas law: \[ PV = nRT \] where: - \( P \) is the pressure in Pascals (Pa), - \( V \) is the volume in cubic meters (m³), - \( n \) is the number of moles of gas, - \( R \) is the gas constant (approximately 8.3145 J/mol·K), - \( T \) is the temperature in Kelvin (K). Given: - Initial volume (\( V_1 \)) = 350.0 cm³ = 0.00035 m³ (converting to cubic meters), - Initial temperature (\( T_1 \)) = 22.0°C = 295 K (converting to Kelvin), - Initial pressure (\( P_1 \)) = 99.3 kPa = 99300 Pa (converting to Pascals), - Final temperature (\( T_2 \)) = 0°C = 273 K (at STP), - Final pressure (\( P_2 \)) = 101.325 kPa = 101325 Pa (at STP). We need to find the final volume (\( V_2 \)) at STP. First, let's calculate the number of moles of helium gas using the ideal gas law at the initial conditions: \[ n = \frac{P_1 V_1}{R T_1} \] Then, we can use the ideal gas law again to find the final volume at STP: \[ V_2 = \frac{n R T_2}{P_2} \] Let's calculate the number of moles of helium gas first. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(99300\times 0.00035\right)}{\left(8.3145\times 295\right)}\) - step1: Remove the parentheses: \(\frac{99300\times 0.00035}{8.3145\times 295}\) - step2: Multiply the numbers: \(\frac{34.755}{8.3145\times 295}\) - step3: Multiply the numbers: \(\frac{34.755}{2452.7775}\) - step4: Convert the expressions: \(\frac{\frac{6951}{200}}{\frac{981111}{400}}\) - step5: Multiply by the reciprocal: \(\frac{6951}{200}\times \frac{400}{981111}\) - step6: Reduce the numbers: \(2317\times \frac{2}{327037}\) - step7: Multiply: \(\frac{2317\times 2}{327037}\) - step8: Multiply: \(\frac{4634}{327037}\) The number of moles of helium gas is approximately 0.01417 moles. Now, let's calculate the final volume at STP. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(0.01417\times 8.3145\times 273\right)}{101325}\) - step1: Remove the parentheses: \(\frac{0.01417\times 8.3145\times 273}{101325}\) - step2: Multiply the terms: \(\frac{32.163894945}{101325}\) - step3: Convert the expressions: \(\frac{\frac{6432778989}{200000000}}{101325}\) - step4: Multiply by the reciprocal: \(\frac{6432778989}{200000000}\times \frac{1}{101325}\) - step5: Reduce the numbers: \(\frac{306322809}{200000000}\times \frac{1}{4825}\) - step6: Multiply the fractions: \(\frac{306322809}{200000000\times 4825}\) - step7: Multiply: \(\frac{306322809}{965000000000}\) The volume of the helium gas at STP is approximately 0.000317 m³ or 317 cm³.