(b) How many milliliters of 0.248 M HCl are needed to react with 1.36 g of zinc to produce hydrogen gas? How many milliliters of hydrogen gas are expected at STP?

To solve this problem, we need to follow these steps: 1. **Determine the moles of zinc (Zn) present in 1.36 g.** 2. **Use the balanced chemical equation to find the moles of HCl required to react with the moles of zinc.** 3. **Calculate the volume of 0.248 M HCl needed.** 4. **Determine the volume of hydrogen gas produced at STP from the moles of zinc reacted.** ### Step 1: Calculate moles of zinc The molar mass of zinc (Zn) is approximately 65.38 g/mol. We can calculate the moles of zinc using the formula: \[ \text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}} \] ### Step 2: Balanced chemical equation The reaction between zinc and hydrochloric acid (HCl) is given by the balanced equation: \[ \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \] From the equation, we see that 1 mole of Zn reacts with 2 moles of HCl. ### Step 3: Calculate moles of HCl needed Using the moles of Zn calculated in Step 1, we can find the moles of HCl required: \[ \text{moles of HCl} = 2 \times \text{moles of Zn} \] ### Step 4: Calculate volume of HCl solution needed Using the concentration of HCl (0.248 M), we can find the volume needed: \[ \text{Volume of HCl (L)} = \frac{\text{moles of HCl}}{\text{concentration of HCl (M)}} \] To convert this volume to milliliters, we multiply by 1000. ### Step 5: Calculate volume of hydrogen gas produced at STP At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Therefore, the volume of hydrogen gas produced can be calculated as: \[ \text{Volume of } H_2 \text{ (L)} = \text{moles of } H_2 \times 22.4 \text{ L/mol} \] Now, let's perform the calculations step by step. 1. Calculate moles of Zn: \[ \text{moles of Zn} = \frac{1.36 \text{ g}}{65.38 \text{ g/mol}} \] 2. Calculate moles of HCl needed: \[ \text{moles of HCl} = 2 \times \text{moles of Zn} \] 3. Calculate volume of HCl needed: \[ \text{Volume of HCl (L)} = \frac{\text{moles of HCl}}{0.248 \text{ M}} \] 4. Convert to milliliters: \[ \text{Volume of HCl (mL)} = \text{Volume of HCl (L)} \times 1000 \] 5. Calculate volume of hydrogen gas produced: \[ \text{Volume of } H_2 \text{ (L)} = \text{moles of Zn} \times 22.4 \text{ L/mol} \] Now, let's perform these calculations. Calculate the value by following steps: - step0: Calculate: \(2\left(\frac{1.36}{65.38}\right)\) - step1: Divide the terms: \(2\times \frac{68}{3269}\) - step2: Multiply: \(\frac{2\times 68}{3269}\) - step3: Multiply: \(\frac{136}{3269}\) Calculate or simplify the expression \( (1.36/65.38)*22.4 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{1.36}{65.38}\right)\times 22.4\) - step1: Divide the terms: \(\frac{68}{3269}\times 22.4\) - step2: Convert the expressions: \(\frac{68}{3269}\times \frac{112}{5}\) - step3: Multiply the fractions: \(\frac{68\times 112}{3269\times 5}\) - step4: Multiply the terms: \(\frac{7616}{3269\times 5}\) - step5: Multiply the terms: \(\frac{7616}{16345}\) - step6: Reduce the fraction: \(\frac{1088}{2335}\) Calculate or simplify the expression \( (2*(1.36/65.38))/0.248 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(2\left(\frac{1.36}{65.38}\right)\right)}{0.248}\) - step1: Remove the parentheses: \(\frac{2\left(\frac{1.36}{65.38}\right)}{0.248}\) - step2: Divide the terms: \(\frac{2\times \frac{68}{3269}}{0.248}\) - step3: Multiply the numbers: \(\frac{\frac{136}{3269}}{0.248}\) - step4: Convert the expressions: \(\frac{\frac{136}{3269}}{\frac{31}{125}}\) - step5: Multiply by the reciprocal: \(\frac{136}{3269}\times \frac{125}{31}\) - step6: Multiply the fractions: \(\frac{136\times 125}{3269\times 31}\) - step7: Multiply: \(\frac{17000}{101339}\) Calculate or simplify the expression \( 1.36/65.38 \). Calculate the value by following steps: - step0: Calculate: \(\frac{1.36}{65.38}\) - step1: Convert the expressions: \(\frac{\frac{34}{25}}{\frac{3269}{50}}\) - step2: Multiply by the reciprocal: \(\frac{34}{25}\times \frac{50}{3269}\) - step3: Reduce the numbers: \(34\times \frac{2}{3269}\) - step4: Multiply: \(\frac{34\times 2}{3269}\) - step5: Multiply: \(\frac{68}{3269}\) Let's summarize the calculations step by step: ### Step 1: Calculate moles of zinc (Zn) \[ \text{moles of Zn} \approx 0.0208 \text{ mol} \] ### Step 2: Calculate moles of HCl needed \[ \text{moles of HCl} \approx 2 \times 0.0208 \approx 0.0416 \text{ mol} \] ### Step 3: Calculate volume of HCl needed \[ \text{Volume of HCl (L)} \approx \frac{0.0416}{0.248} \approx 0.1678 \text{ L} \] Converting to milliliters: \[ \text{Volume of HCl (mL)} \approx 0.1678 \times 1000 \approx 167.8 \text{ mL} \] ### Step 4: Calculate volume of hydrogen gas produced at STP \[ \text{Volume of } H_2 \text{ (L)} \approx 0.0208 \times 22.4 \approx 0.4659 \text{ L} \] Converting to milliliters: \[ \text{Volume of } H_2 \text{ (mL)} \approx 0.4659 \times 1000 \approx 465.9 \text{ mL} \] ### Final Results - **Volume of 0.248 M HCl needed:** approximately **167.8 mL** - **Volume of hydrogen gas produced at STP:** approximately **465.9 mL**