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kreshnik
 Post subject: Task! Chemistry.
PostPosted: Mon, 26 Dec 2011 19:37:16 UTC 
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How should I solve this one??!!
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outermeasure
 Post subject: Re: Task! Chemistry.
PostPosted: Tue, 27 Dec 2011 01:15:44 UTC 
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kreshnik wrote:
https://8842006143235788137-a-1802744773732722657-s-sites.googlegroups.com/site/fisnikib/Home/KRESHNIIKKKK.bmp?attachauth=ANoY7cpBgpJheZ5iRu0rqD31IOmhhehkyvtEcnW4wuQcol-0n-N7AREZ3ffOMrJVkqpD2fg6up-aaMACjHWZmXIqqXQlkVUkO81KNW40c9KEoQ8IszHfb_VdiJtgIRZBYlk9Vg1QDY1FO_BirbuX-IvaJhk4EoMdXCSJjRT3FwQzS61D--p2qznFSagtHntQNsTkpWsqiVx3kH4yPjVyR01RaAT1SCWa-A%3D%3D&attredirects=0

How should I solve this one??!!


You need to know the pK_a value.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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kreshnik
 Post subject: Re: Task! Chemistry.
PostPosted: Tue, 27 Dec 2011 14:37:26 UTC 
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sorry... my fault :(

0.1 mol \:\: CH3COOH

[H^+]=?\:\:\:\:\:pH=?

pKa=4.75

Ka=1.8*10^{-5}
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outermeasure
 Post subject: Re: Task! Chemistry.
PostPosted: Wed, 28 Dec 2011 01:12:59 UTC 
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kreshnik wrote:
sorry... my fault :(

0.1 mol \:\: CH3COOH

[H^+]=?\:\:\:\:\:pH=?

pKa=4.75

Ka=1.8*10^{-5}


Remember we have the equilibrium \mathrm{{CH_3COOH}_{(aq)}}+\mathrm{{H_2O}_{(l)}} \rightleftharpoons\mathrm{{H_3O}^+_{(aq)}}+\mathrm{{CH_3COO}^-_{(aq)}}, and the acid dissociation constant K_a=\dfrac{[\mathrm{{H_3O}^+_{(aq)}}][\mathrm{{CH_3COO}^-_{(aq)}}]}{[\mathrm{{CH_3COOH}_{(aq)}}]}. Now solve a quadratic equation and hence \mathrm{pH}=-\log_{10}[\mathrm{{H_3O}^+_{(aq)}}].

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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kreshnik
 Post subject: Re: Task! Chemistry.
PostPosted: Wed, 28 Dec 2011 11:05:18 UTC 
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Thanks a lot :D
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