InterviewSolution
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InterviewSolution
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A vessel contains a mixture of `7 g` of nitrogen and `11 g` carbon dioxide at temperature ` T = 290 K`. If pressure of the mixure is `1 atm (= 1.01 xx 10^5 N//m^2)`, calculate its density `(R = 8.31 J//mol - K)`. |
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Answer» We know, for the mixture, `N_2` and `CO_2` (being regarded as ideal gases, their mixture too behaves like an ideal gas) `p V = v R T`, so `p_0 V = v R T` Where, `v` is the total number of moles of the gases (mixture) present and `V` is the volume of the vessel. If `v_1` and `v_2` are number of moles of `N_2` and `CO_2` respectively present in the mixture, then `v = v_1 + v_2` Now number of moles of `N_2` and `CO_2` is, by definition, given by `v_1 = (m_1)/(M_1)` and, `v_2 = (m_2)/(M_2)` where, `m_1` is the mass of `N_2` (Moleculer weight `= M_1`) in the mixture and `m_2` is the mass of `CO_2` (Molecular weight `= M_2`) in the mixture. Therefore density of the mixture is given by `rho = (m_1 + m_2)/(V) = (m_1 + m_2)/((v RT//P_0))` =`(p_0)/(RT).(m_1 + m_2)/(v_1 + v_2) = (p_0(m_1 + m_2)M_1 M_2)/(RT(m_1 M_2 +m_2 M_1))` =`1.5 kg//m^3` on substitution. |
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