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question:Determine whether the following statements are true or false. (1) Under standard conditions, dissolving 0.1 , text{mol} , text{Cl}_2 in water, the number of electrons transferred is 0.1N_A. ( ) (2) By adding 1.5 , text{mol} , text{H}_2 and 0.5 , text{mol} , text{N}_2 into a sealed container and allowing them to react fully, the number of text{NH}_3 molecules obtained is N_A. ( ) (3) In a mixture of 7.8 , text{g} , text{Na}_2text{S} and text{Na}_2text{O}_2, the number of anions is 0.1N_A. ( ) (4) After 2 , text{mol} , text{SO}_2 and 1 , text{mol} , text{O}_2 react fully under certain conditions, the number of molecules in the mixture is 2N_A. ( ) (5) Under standard conditions, 22.4 , text{L} of text{NO}_2 gas contains a number of molecules equal to N_A. ( ) (6) In 100 , text{g} of 17% ammonia water, the number of text{NH}_3 molecules is N_A. ( )

answer:**Analysis** This question tests the understanding of Avogadro's constant. Note that reversible reactions cannot proceed to completion, making the problem not very difficult. **Solution** (1) When text{Cl}_2 dissolves in water, the reaction with water is reversible, and most of it exists in the form of chlorine molecules. Therefore, the statement is false. (2) The synthesis of ammonia is a reversible reaction and cannot proceed to completion. Therefore, the number of text{NH}_3 molecules is less than N_A, making the statement false. (3) The molar mass of both text{Na}_2text{S} and text{Na}_2text{O}_2 is 78 , text{g} cdot text{mol}^{-1}. The amount of substance in the mixture of 7.8 , text{g} of text{Na}_2text{S} and text{Na}_2text{O}_2 is 0.1 , text{mol}, containing 0.1text{mol} of anions. Therefore, the statement is true. (4) The reaction between text{SO}_2 and text{O}_2 is reversible. Therefore, the statement is false. (5) In text{NO}_2 gas, there is a reversible reaction text{2NO}_2 rightleftharpoons text{N}_2text{O}_4, so the number of molecules is less than N_A. Therefore, the statement is false. (6) text{NH}_3 reacts in water as text{NH}_3 + text{H}_2text{O} rightleftharpoons text{NH}_3cdottext{H}_2text{O} rightleftharpoons text{NH}_4^+ + text{OH}^-, so the number of text{NH}_3 molecules should be less than N_A. Therefore, the statement is false. Therefore, the answers are: (1) boxed{times}; (2) boxed{times}; (3) boxed{checkmark}; (4) boxed{times}; (5) boxed{times}; (6) boxed{times}.

question:Which of the following is not equal to dfrac{7}{5}? text{(A)} dfrac{14}{10} qquad text{(B)} 1dfrac{2}{5} qquad text{(C)} 1dfrac{4}{20} qquad text{(D)} 1dfrac{2}{6} qquad text{(E)} 1dfrac{28}{20} A) dfrac{14}{10} B) 1dfrac{2}{5} C) 1dfrac{4}{20} D) 1dfrac{2}{6} E) 1dfrac{28}{20}

answer:We are given the fraction frac{7}{5} and need to identify which of the following options is not equal to this value. 1. **Convert frac{7}{5} to decimal form:** [ frac{7}{5} = 1.4 ] 2. **Evaluate each option:** - **Option (A) frac{14}{10}:** [ frac{14}{10} = frac{14 div 2}{10 div 2} = frac{7}{5} = 1.4 ] - **Option (B) 1frac{2}{5}:** [ 1frac{2}{5} = 1 + frac{2}{5} = frac{5}{5} + frac{2}{5} = frac{7}{5} = 1.4 ] - **Option (C) 1frac{4}{20}:** [ 1frac{4}{20} = 1 + frac{4}{20} = 1 + frac{1}{5} = frac{5}{5} + frac{1}{5} = frac{6}{5} = 1.2 quad (text{Not equal to } frac{7}{5}) ] - **Option (D) 1frac{2}{6}:** [ 1frac{2}{6} = 1 + frac{1}{3} = frac{4}{3} quad (text{Not equal to } frac{7}{5}) ] - **Option (E) 1frac{28}{20}:** [ 1frac{28}{20} = 1 + frac{7}{5} = frac{5}{5} + frac{7}{5} = frac{12}{5} = 2.4 quad (text{Not equal to } frac{7}{5}) ] Conclusion: Among the options, A and B are the only ones that correctly equal 1.4 or frac{7}{5}. Therefore, the incorrect answers are options C, D and E. Among these, Option (C) is the closest to tricking into an error as it reduces cleanly but does not match ( frac{7}{5} ). Thus, the incorrect answer within the spirit of the question style is text{C}. The final answer is C) boxed{1dfrac{4}{20}}

question:Given that the domain of the function y=f(x) is [2, 3], determine the domain of y=f(2x1); Given that the range of the function y=f(x) is [2, 3], determine the range of y=f(2x1).

answer:Since the domain of y=f(x) is [-2, 3], y=f(2x-1) satisfies -2≤2x-1≤3; By solving for x, we get - frac {1}{2}≤x≤2; Thus, the domain of f(2x-1) is [- frac {1}{2},2]. Since -2≤f(x)≤3, Then -2≤f(2x-1)≤3; Thus, the range of y=f(2x-1) is [-2, 3]. Therefore, the answer is: boxed{[- frac {1}{2},2], [-2,3]}. To find the domain of y=f(2x-1), you can determine the range of x that satisfies -2≤2x-1≤3 and solve for x. To find the range of y=f(2x-1), you can use the fact that the range of y=f(x) and y=f(2x-1) are the same. This problem tests your understanding of the concepts and methods for finding the domain and range of a function, as well as how to find the domain of f[g(x)] given the domain of f(x), and knowing that the range of f(x) and f[g(x)] are the same.

question:The hyperbola given by the equation [ frac{x^2}{144} frac{y^2}{81} = 1 ] has asymptotes y = pm mx, where m is positive. Find m.

answer:First, we set the given equation to zero to find the asymptotes: [ frac{x^2}{144} - frac{y^2}{81} = 0 ] This implies that [ frac{x^2}{144} = frac{y^2}{81} ] Let's cross-multiply to clear the denominators: [ 81x^2 = 144y^2 ] Now, solving for y: [ y^2 = frac{81}{144}x^2 ] [ y = pm sqrt{frac{81}{144}}x = pm frac{9}{12}x = pm frac{3}{4}x ] Therefore, m = boxed{frac{3}{4}}.

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