x$x$ mg of pure HCl was used to make an aqueous solution. 25.0 mL of 0.1M Ba(OH)₂$Ba(OH)_{2}$ solution is used when the HCl solution was titrated against it.
The numerical value of x$x$ is ____ × 10⁻¹$\times 10^{-1}$ (Nearest integer)
Given : Molar mass of HCl and Ba(OH)₂$Ba(OH)_{2}$ are 36.5 and 171.0 g mol⁻¹$171.0 \text{ g mol}^{-1}$ respectively.
Numerical Answer Type:
Enter a numerical valueAnswer: 1825 to 1825+4 marks
Solution & Explanation
Related Formula
N₁ V₁ = N₂ V₂$$N_1 V_1 = N_2 V_2$$
Equivalents of Acid = Equivalents of Base
Core Logic
Write the balanced chemical equation to find the molar ratio, or use the concept of equivalents directly. Barium hydroxide is a diacidic base (n$n$-factor = 2) and hydrochloric acid is a monobasic acid (n$n$-factor = 1).
Millimoles of Ba(OH)₂ = M × V = 0.1 M × 25.0 mL = 2.5 mmoles$Ba(OH)_2 = M \times V = 0.1 \text{ M} \times 25.0 \text{ mL} = 2.5 \text{ mmoles}$.
Since 1 mole of Ba(OH)₂$Ba(OH)_2$ neutralizes 2 moles of HCl$HCl$:
Millimoles of HCl = 2 × 2.5 = 5.0 mmoles$HCl = 2 \times 2.5 = 5.0 \text{ mmoles}$.
Step 2: Calculating Mass
Weight of HCl = mmoles × molar mass (mg/mmol)$HCl = \text{mmoles} \times \text{molar mass (mg/mmol)}$
Weight = 5.0 × 36.5 = 182.5 mg$5.0 \times 36.5 = 182.5 \text{ mg}$.
Step 3: Matching Format
We need the answer in the form of x × 10⁻¹$x \times 10^{-1}$ mg.
182.5 mg = 1825 × 10⁻¹ mg$182.5 \text{ mg} = 1825 \times 10^{-1} \text{ mg}$.
Thus, x = 1825$x = 1825$.
Acid-Base Titration and Stoichiometry diagram for Q73 - JEE Main 2026 Morning
Pattern Recognition
Always multiply the Molarity by the n-factor to get Normality when performing titrations. 0.1 M Ba(OH)₂ = 0.2 N$0.1 \text{ M } Ba(OH)_2 = 0.2 \text{ N}$. Equivalents = 0.2 × 25 = 5 meq$0.2 \times 25 = 5 \text{ meq}$. Mass = 5 × 36.5 = 182.5 mg$5 \times 36.5 = 182.5 \text{ mg}$.
Chapter Mix
Class 11 Chemistry: Some Basic Concepts of Chemistry
Class 12 Chemistry: Solutions
Keywords:#aqueous solution#JEE Main 2026 Morning Q73#Some Basic Concepts of Chemistry JEE Main 2026#Acid-Base Titration and Stoichiometry JEE Main 2026
More Some Basic Concepts of Chemistry Previous-Year Questions — Page 6
Qjee_main_2024_29_january_eveningVolumetric Titration and Molarity
If 50 mL$50\text{ mL}$ of 0.5 M$0.5\text{ M}$ oxalic acid is required to neutralise 25 mL$25\text{ mL}$ of NaOH$\mathrm{NaOH}$ solution, the amount of NaOH$\mathrm{NaOH}$ in 50 mL$50\text{ mL}$ of given NaOH$\mathrm{NaOH}$ solution is ________ g.
For oxalic acid (H₂C₂O₄$\text{H}_2\text{C}_2\text{O}_4$), the valence factor (n$n$-factor) is 2$2$. For NaOH$\text{NaOH}$, the n$n$-factor is 1$1$.
Substituting the values into the normality equivalence expression:
Remember to use the correct n$n$-factor (2$2$) for dibasic oxalic acid during equivalence matching to avoid calculation errors.
Chapter Mix
Class 11 Chemistry: Some Basic Concepts of Chemistry
Q83jee_main_2024_27_jan_morningStoichiometry
Mass of methane required to produce 22 g$22\text{ g}$ of CO₂$\text{CO}_2$ after complete combustion is $\text{\quad\quad}$ g.
(Given Molar mass in g mol⁻¹$\text{g mol}^{-1}$: C=12.0$\text{C}=12.0$, H=1.0$\text{H}=1.0$, O=16.0$\text{O}=16.0$)
Molar Mass of CO₂ = 12 + (2 × 16) = 44 g mol⁻¹$$\text{Molar Mass of CO}_2 = 12 + (2 \times 16) = 44\text{ g mol}^{-1}$$Moles of CO₂ produced = (22)/(44) = 0.5 moles$$\text{Moles of CO}_2 \text{ produced} = \frac{22}{44} = 0.5\text{ moles}$$
Step 2: Relate to input mass via stoichiometry metrics
From the balanced equation, 1 mole of CH₄$1\text{ mole of CH}_4$ produces 1 mole of CO₂$1\text{ mole of CO}_2$.
Required Moles of CH₄ = 0.5 moles$$\text{Required Moles of CH}_4 = 0.5\text{ moles}$$Molar Mass of CH₄ = 12 + (4 × 1) = 16 g mol⁻¹$$\text{Molar Mass of CH}_4 = 12 + (4 \times 1) = 16\text{ g mol}^{-1}$$Mass of CH₄ = 0.5 × 16 = 8 g$$\text{Mass of CH}_4 = 0.5 \times 16 = 8\text{ g}$$
Pattern Recognition
22 g of CO₂$22\text{ g of CO}_2$ is exactly half a mole. By stoichiometry ratios, half a mole of methane is needed, which translates to 8 g$8\text{ g}$.
Chapter Mix
Class 11 Chemistry: Some Basic Concepts of Chemistry
Q88jee_main_2024_30_jan_morningMole Concept
0.05 cm$0.05\text{ cm}$ thick coating of silver is deposited on a plate of 0.05 m²$0.05\text{ m}^2$ area. The number of silver atoms deposited on plate are ________ × 10²³$\times 10^{23}$.
(At mass Ag=108, d=7.9 g cm⁻³$Ag=108, d=7.9\text{ g cm}^{-3}$)
Numerical Answer.Answer: 11 to 11
Solution
Related Formula
Volume = Area × Thickness$$\text{Volume} = \text{Area} \times \text{Thickness}$$Mass = Density × Volume$$\text{Mass} = \text{Density} \times \text{Volume}$$Moles = MassMolar Mass$$\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$$Number of Atoms = Moles × NA$$\text{Number of Atoms} = \text{Moles} \times N_A$$
Mass = Volume ×$\times$ Density = 25 cm³ × 7.9 g/cm³ = 197.5 g$25 \text{ cm}^3 \times 7.9 \text{ g/cm}^3 = 197.5 \text{ g}$
Moles of Ag = (197.5)/(108) = 1.8287 moles$\frac{197.5}{108} = 1.8287 \text{ moles}$
Step 3: Calculate Number of Atoms
Number of Atoms = 1.8287 × 6.022 × 10²³$$\text{Number of Atoms} = 1.8287 \times 6.022 \times 10^{23}$$= 11.01 × 10²³$$= 11.01 \times 10^{23}$$
Rounding to nearest integer, we get 11$11$.
Chapter Mix
Class 11 Chemistry: Some Basic Concepts of Chemistry
Class 12 Chemistry: Electrochemistry
Q62jee_main_2024_31_jan_eveningStoichiometry and Calculations
A sample of CaCO₃$CaCO_3$ and MgCO₃$MgCO_3$ weighed 2.21 g$2.21\text{ g}$ is ignited to constant weight of 1.152 g$1.152\text{ g}$. The composition of mixture is:
(Given molar mass in g mol⁻¹$\mathrm{g\,mol^{-1}}$CaCO₃:100, MgCO₃:84$\mathrm{CaCO_3:100, MgCO_3:84}$)
Let the weight of CaCO₃$\mathrm{CaCO}_3$ be x g$x\text{ g}$.
Then, the weight of MgCO₃ = (2.21 - x) g$\mathrm{MgCO}_3 = (2.21 - x)\text{ g}$.
Moles of CaCO₃$\mathrm{CaCO}_3$ decomposed = Moles of CaO$\mathrm{CaO}$ formed.
(x)/(100) = Moles of CaO formed$\frac{x}{100} = \text{Moles of CaO formed}$Weight of CaO formed = (x)/(100) × 56$\text{Weight of CaO formed} = \frac{x}{100} \times 56$
Moles of MgCO₃$\mathrm{MgCO}_3$ decomposed = Moles of MgO$\mathrm{MgO}$ formed.
((2.21 - x))/(84) = Moles of MgO formed$\frac{(2.21 - x)}{84} = \text{Moles of MgO formed}$Weight of MgO formed = (2.21 - x)/(84) × 40$\text{Weight of MgO formed} = \frac{2.21 - x}{84} \times 40$
Step 1: Setting up the Equation
The total weight of the residue (CaO$\mathrm{CaO}$ + MgO$\mathrm{MgO}$) is given as 1.152 g$1.152\text{ g}$.
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