Answer
To react with 1.36 g of zinc, you need approximately 167.8 mL of 0.248 M HCl. This reaction will produce about 465.9 mL of hydrogen gas at STP.
Solution
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**
Answered by UpStudy AI and reviewed by a Professional Tutor
Explain
Simplify this solution
