Determine the apparent molar mass of a mixture of oxygen (2 kg)with nitrogen (3kg),kg/mol 0.295 2947 0.0295 2947 2947

the apparent molar mass of the mixture, we need to calculate the total mass of the mixture and the total number of moles of each component.<br /><br />Given:<br />- Mass of oxygen = 2 kg<br />- Mass of nitrogen = 3 kg<br /><br />First, let's calculate the number of moles of each component using their respective molar masses:<br />- Molar mass of oxygen (O₂) = 32 g/mol<br />- Molar mass ofN₂) = 28 g/mol<br /><br />Number of moles of oxygen:<br />\[ \text{Moles of O₂} = \frac{\text{Mass of O₂}}{\text{Molar mass of O₂}} = \frac{2000 \text{ g}}{32 \text{ g/mol}} = 62.5 \text{ mol} \]<br /><br />Number of moles of nitrogen:<br />\[ \text{Moles of N₂} = \frac{\text{Mass of N₂}}{\text{Molar mass of N₂}} = \frac{3000 \text{ g}}{28 \text{ g/mol}} = 107.1 \text{ mol} \]<br /><br />Next, we calculate the total mass of the mixture:<br />\[ \text{Total mass} = \text{Mass of O₂} + \text{Mass of N₂} = 2000 \text{ g} + 3000 \text{ g} = 5000 \text{ g} = 5 \text{ kg} \]<br /><br />Now, we calculate the total number of moles in the mixture:<br />\[ \text{Total moles} = \text{Moles of O₂} + \text{Moles of N₂} = 62.5 \text{ mol} + 107.1 \text{ mol} = 169.6 \text{ mol} \]<br /><br />Finally, we calculate the apparent molar mass of the mixture:<br />\[ \text{Apparent molar mass} = \frac{\text{Total mass}}{\text{Total moles}} = \frac{5000 \text{ g}}{169.6 \text{ mol}} \approx 29.47 \text{ g/mol} \]<br /><br />Therefore, the correct answer is:<br />\[ \boxed{29.47 \text{ kg/mol}} \]