assuming no determinate errors, within what range are you at 95% confident
level that the true mean value of the calcium content falls.
(4 marks)
b) describe three major steps in a qualitative analysis of heavy metals in soil
samples.
(6 marks)
c) 0.470g of sample containing sodium carbonate was treated with 50ml of 0.10m
hcl. the excess hcl was back titrated using 0.1m standardized naoh were
20ml of naoh was used. calculate the percentage na₂co₃ in the sample. (rfm
of na₂co₃ = 105.99g/mol)
(5 marks)
d) calculate the ph of 4.0 x10⁻⁴m and 0.001m solutions of ethanoic acid given that
its kₐ= 1.8 x10⁻⁵
(5 marks)
question four
a) describe how the following solutions are prepared in the laboratory, show all your
workings:
i) 500ml of 0.6m hydrochloric acid (density of hcl = 1.18g/cm³,
h=1.007, cl= 35.456, %purity = 37%)
(3 marks)
ii) 400ml of 0.5m sodium carbonate na₂co₃
(2 marks)
iii) 500ml of 2.0m nitric acid (n=15.00, o = 15.999, %purity = 63%, density
of hno₃= 1.51g/cm³)
(2 marks)

Question

assuming no determinate errors, within what range are you at 95% confident
level that the true mean value of the calcium content falls.
(4 marks)
b) describe three major steps in a qualitative analysis of heavy metals in soil
samples.
(6 marks)
c) 0.470g of sample containing sodium carbonate was treated with 50ml of 0.10m
hcl. the excess hcl was back titrated using 0.1m standardized naoh were
20ml of naoh was used. calculate the percentage na₂co₃ in the sample. (rfm
of na₂co₃ = 105.99g/mol)
(5 marks)
d) calculate the ph of 4.0 x10⁻⁴m and 0.001m solutions of ethanoic acid given that
its kₐ= 1.8 x10⁻⁵
(5 marks)
question four
a) describe how the following solutions are prepared in the laboratory, show all your
workings:
 i) 500ml of 0.6m hydrochloric acid (density of hcl = 1.18g/cm³,
h=1.007, cl= 35.456, %purity = 37%)
(3 marks)
 ii) 400ml of 0.5m sodium carbonate na₂co₃
(2 marks)
 iii) 500ml of 2.0m nitric acid (n=15.00, o = 15.999, %purity = 63%, density
of hno₃= 1.51g/cm³)
(2 marks)

Accepted Answer

### Part c)
# Explanation:
## Step 1: Determine moles of HCl initially
Molarity of HCl, $ M_{HCl} = 0.10 \, M $, volume of HCl, $ V_{HCl} = 50 \, mL = 0.05 \, L $.
Moles of HCl, $ n_{HCl} = M_{HCl} \times V_{HCl} = 0.10 \, mol/L \times 0.05 \, L = 0.005 \, mol $.

## Step 2: Determine moles of NaOH used
Molarity of NaOH, $ M_{NaOH} = 0.1 \, M $, volume of NaOH, $ V_{NaOH} = 20 \, mL = 0.02 \, L $.
Moles of NaOH, $ n_{NaOH} = M_{NaOH} \times V_{NaOH} = 0.1 \, mol/L \times 0.02 \, L = 0.002 \, mol $.

## Step 3: Moles of HCl reacted with $ Na_2CO_3 $
HCl and NaOH react in 1:1 ratio ($ HCl + NaOH = NaCl + H_2O $). So moles of HCl reacted with NaOH is 0.002 mol.
Moles of HCl reacted with $ Na_2CO_3 $, $ n_{HCl(reacted\ with\ Na_2CO_3)} = 0.005 - 0.002 = 0.003 \, mol $.

## Step 4: Moles of $ Na_2CO_3 $
Reaction: $ Na_2CO_3 + 2HCl = 2NaCl + H_2O + CO_2 $. So 1 mol $ Na_2CO_3 $ reacts with 2 mol HCl.
Moles of $ Na_2CO_3 $, $ n_{Na_2CO_3} = \frac{n_{HCl(reacted\ with\ Na_2CO_3)}}{2} = \frac{0.003}{2} = 0.0015 \, mol $.

## Step 5: Mass of $ Na_2CO_3 $
RFM of $ Na_2CO_3 = 105.99 \, g/mol $.
Mass of $ Na_2CO_3 $, $ m = n \times RFM = 0.0015 \, mol \times 105.99 \, g/mol = 0.158985 \, g $.

## Step 6: Percentage of $ Na_2CO_3 $
Percentage $ = \frac{mass\ of\ Na_2CO_3}{mass\ of\ sample} \times 100 = \frac{0.158985}{0.470} \times 100 \approx 33.83\% $.

# Answer: Approximately $ 33.83\% $

### Part d)
For ethanoic acid ($ CH_3COOH $), $ K_a = 1.8 \times 10^{-5} $, formula for pH of weak acid: $ pH = \frac{1}{2}(pK_a - \log c) $, where $ c $ is concentration.

#### For $ c = 4.0 \times 10^{-3} \, M $:
## Step 1: Calculate $ pK_a $
$ pK_a = -\log K_a = -\log(1.8 \times 10^{-5}) \approx 4.74 $.

## Step 2: Calculate pH
$ pH = \frac{1}{2}(4.74 - \log(4.0 \times 10^{-3})) $.
$ \log(4.0 \times 10^{-3}) = \log 4 + \log 10^{-3} \approx 0.602 - 3 = -2.398 $.
$ pH = \frac{1}{2}(4.74 - (-2.398)) = \frac{1}{2}(7.138) \approx 3.57 $.

#### For $ c = 0.001 \, M = 1.0 \times 10^{-3} \, M $:
## Step 1: Calculate $ \log c $
$ \log(1.0 \times 10^{-3}) = -3 $.

## Step 2: Calculate pH
$ pH = \frac{1}{2}(4.74 - (-3)) = \frac{1}{2}(7.74) \approx 3.87 $.

# Answer:
- For $ 4.0 \times 10^{-3} \, M $: $ \approx 3.57 $
- For $ 0.001 \, M $: $ \approx 3.87 $

### Question Four a) i)
# Explanation:
## Step 1: Calculate mass of HCl needed
Molarity $ M = 0.6 \, M $, volume $ V = 500 \, mL = 0.5 \, L $.
Moles of HCl, $ n = M \times V = 0.6 \, mol/L \times 0.5 \, L = 0.3 \, mol $.
Molar mass of HCl, $ M_{HCl} = 1 + 35.456 = 36.456 \, g/mol $.
Mass of pure HCl, $ m_{pure} = n \times M_{HCl} = 0.3 \times 36.456 = 10.9368 \, g $.

## Step 2: Calculate mass of commercial HCl needed
Purity = 37%, so $ \text{Mass of commercial HCl} = \frac{m_{pure}}{\text{purity}} = \frac{10.9368}{0.37} \approx 29.56 \, g $.

## Step 3: Calculate volume of commercial HCl
Density $
ho = 1.18 \, g/cm^3 $, volume $ V = \frac{\text{mass}}{
ho} = \frac{29.56}{1.18} \approx 25.05 \, mL $.

## Step 4: Preparation steps
1. Measure ~25.05 mL of commercial HCl using a graduated cylinder.
2. Transfer to a 500 mL volumetric flask.
3. Add distilled water to the mark, mix well.

# Answer:
- Volume of 37% HCl needed: ~25.05 mL.
- Steps: Measure, transfer, dilute to 500 mL.

### Question Four a) ii)
# Explanation:
## Step 1: Calculate moles of $ Na_2CO_3 $
Molarity $ M = 0.5 \, M $, volume $ V = 400 \, mL = 0.4 \, L $.
Moles of $ Na_2CO_3 $, $ n = M \times V = 0.5 \times 0.4 = 0.2 \, mol $.

## Step 2: Calculate mass of $ Na_2CO_3 $
Molar mass of $ Na_2CO_3 = 105.99 \, g/mol $.
Mass, $ m = n \times M = 0.2 \times 105.99 = 21.198 \, g $.

## Step 3: Preparation steps
1. Weigh 21.20 g of $ Na_2CO_3 $ (anhydrous) using a balance.
2. Transfer to a 400 mL volumetric flask (or dissolve in beaker, then transfer).
3. Add distilled water to the mark, mix well.

# Answer:
- Mass of $ Na_2CO_3 $: ~21.20 g.
- Steps: Weigh, transfer, dilute to 400 mL.

### Question Four a) iii)
# Explanation:
## Step 1: Calculate moles of $ HNO_3 $
Molarity $ M = 2.0 \, M $, volume $ V = 500 \, mL = 0.5 \, L $.
Moles of $ HNO_3 $, $ n = M \times V = 2.0 \times 0.5 = 1.0 \, mol $.

## Step 2: Calculate mass of pure $ HNO_3 $
Molar mass of $ HNO_3 = 1 + 15 + 3 \times 16 = 63 \, g/mol $.
Mass of pure $ HNO_3 $, $ m_{pure} = n \times M = 1.0 \times 63 = 63 \, g $.

## Step 3: Calculate mass of commercial $ HNO_3 $
Purity = 63%, so $ \text{Mass of commercial } HNO_3 = \frac{m_{pure}}{\text{purity}} = \frac{63}{0.63} = 100 \, g $.

## Step 4: Calculate volume of commercial $ HNO_3 $
Density $
ho = 1.51 \, g/cm^3 $, volume $ V = \frac{\text{mass}}{
ho} = \frac{100}{1.51} \approx 66.23 \, mL $.

## Step 5: Preparation steps
1. Measure ~66.23 mL of commercial $ HNO_3 $ using a graduated cylinder.
2. Transfer to a 500 mL volumetric flask.
3. Add distilled water to the mark, mix well.

# Answer:
- Volume of 63% $ HNO_3 $ needed: ~66.23 mL.
- Steps: Measure, transfer, dilute to 500 mL.

### Part b)
# Brief Explanations:
1. **Sample Preparation**: Collect soil sample, dry, grind, sieve to homogenize. Digest with acid (e.g., $ HNO_3/HCl $) to extract heavy metals into solution, filter to remove debris.
2. **Separation/Concentration**: Use techniques like precipitation (e.g., sulfide for $ Pb^{2+}, Cu^{2+} $), ion exchange, or solvent extraction to separate/ concentrate heavy metals from matrix.
3. **Detection/Identification**: Use methods like flame AAS (identify $ Na, K, Ca $), UV - Vis (for colored complexes), or spot tests (e.g., dithizone for $ Hg^{2+}, Cd^{2+} $) to detect and identify heavy metals.

# Answer:
1. Sample preparation (digestion, homogenization).
2. Separation/concentration (precipitation, extraction).
3. Detection/identification (AAS, spot tests).

### Part a (Confidence Interval, assuming data for calcium content is missing, but general steps):
# Explanation:
## Step 1: Recall confidence interval formula
For sample mean $ \bar{x} $, standard deviation $ s $, sample size $ n $, 95% CI: $ \bar{x} \pm t_{\alpha/2, n - 1} \times \frac{s}{\sqrt{n}} $ (t - distribution) or $ \bar{x} \pm z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}} $ (z - distribution, if $ \sigma $ known).

## Step 2: Assume sample stats (e.g., $ \bar{x} $, $ s $, $ n $)
Suppose $ \bar{x} = \mu_{sample} $, $ s $ (sample SD), $ n $ (sample size). Find $ t_{0.025, n - 1} $ (or $ z_{0.025} = 1.96 $ for large $ n $).

## Step 3: Calculate margin of error (ME)
$ ME = t_{\alpha/2, n - 1} \times \frac{s}{\sqrt{n}} $ (or $ z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}} $).

## Step 4: Confidence interval
$ CI = (\bar{x} - ME, \bar{x} + ME) $.

# Answer:
Range: $ \bar{x} \pm t_{\alpha/2, n - 1} \times \frac{s}{\sqrt{n}} $ (or $ z $ - based) around sample mean. (Requires sample data for numerical range.)

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QUESTION IMAGE

Question

Explanation:

Part c)

Step 1: Determine moles of HCl initially

Step 2: Determine moles of NaOH used

Step 3: Moles of HCl reacted with \( Na_2CO_3 \)

Step 4: Moles of \( Na_2CO_3 \)

Step 5: Mass of \( Na_2CO_3 \)

Step 6: Percentage of \( Na_2CO_3 \)

Step 1: Calculate mass of HCl needed

Step 2: Calculate mass of commercial HCl needed

Step 3: Calculate volume of commercial HCl

Step 4: Preparation steps

Step 1: Calculate moles of \( Na_2CO_3 \)

Step 2: Calculate mass of \( Na_2CO_3 \)

Step 3: Preparation steps

Answer:

Part d)

For \( c = 4.0 \times 10^{-3} \, M \):

Step 1: Calculate \( pK_a \)

Step 2: Calculate pH

For \( c = 0.001 \, M = 1.0 \times 10^{-3} \, M \):

Step 1: Calculate \( \log c \)

Step 2: Calculate pH