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Bài 6 trang 47 SGK Toán 11 tập 2 - Cánh Diều

Chỉ số hay độ pH của một dung dịch được tính theo công thức: \(pH = - \log [{H^ + }]\).

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Đề bài

Chỉ số hay độ pH của một dung dịch được tính theo công thức: \(pH =  - \log [{H^ + }]\). Phân tích nồng độ ion hydrogen \([{H^ + }]\) trong hai mẫu nước sông, ta có kết quả sau: Mẫu 1: \([{H^ + }] = {8.10^{ - 7}}\), Mẫu 2: ꧂\([{H^ + }] = {2.10^{ - 9}}\). Không dùng máy tính cầm tay, hãy so sánh độ pH của hai mẫu nước trên.

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

+ Mẫu 1: \(pH =  - \log [{H^ + }] =  - \log \left( {{{8.10}^{ - 7}}} \right) =  - \log 8 - \log {10^{ - 7}} =  - \log 8 + 7\log 10 =  - \log 8 + 7 =  - 3\log 2 + 7\)+ Mẫu 2: \(pH =  - \log [{H^ + }] =  - \log \left( {{{2.10}^{ - 9}}} \right) =  - \log 2 - \log {10^{ - 9}} =  - \log 2 + 9\)Do \(3\log 2 > \log 2 \Rightarrow  - 3\log 2 <  - \log 2 \Rightarrow  - 3\log 2 + 7 <  - \log 2 + 7 \Rightarrow  - 3\log 2 <  - \log 2 + 9\)=> Độ pH của mẫu 2 lớn hơn độ pH của mẫu 1.

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