Course: 17.9 量度测量 | The Way To Learn

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量度测量
How many calories are in your food?
::你的食物里有多少卡路里?

At one time, calories in foods were measured with a bomb calorimeter (see figure above). A weighed amount of the food would be placed in the calorimeter and the system was then sealed and filled with oxygen. An electric spark ignited the food-oxygen . The amount of released when the food burned would give an idea of the food calories present. Today calories are calculated from the , , and fat content of the food (all determined by chemical analysis). No more bombs needed.
::有一次,用炸弹卡路里测量了食物的卡路里(见上图),将相当量的食物放在卡路里,然后将系统密封并装满氧气,电火点燃了食物氧气。烧食物时释放的热量将使人们了解食物的热量。今天,根据食物的含量、热量和脂肪量计算出食物的卡路里(全部由化学分析确定)。不需要更多炸弹。

Calorimetry
::量度测量

Calorimetry is the measurement of the transfer of heat into or out of a system during a or physical process. A calorimeter is an insulated container that is used to measure heat changes. The majority of reactions that can be analyzed in a calorimetry are either or aqueous solutions . A frequently used and inexpensive calorimeter is a set of nested foam cups fitted with a lid to limit the heat exchange between the liquid in the cup and the air in the surroundings (see Figure ). In a typical calorimetry experiment, specific volumes of the reactants are dispensed into separate containers and the temperature of each is measured. They are then mixed into the calorimeter, which starts the reaction. The reactant mixture is stirred until the reaction is complete, while the temperature of the reaction is continuously monitored.
::热量测量是测量在一种或物理过程中热向一个系统或从一个系统中转移热量的量度,热量计是用来测量热变化的隔热容器,在热量测量中可以分析的大多数反应是要么或水溶解物。经常使用和廉价的热量计是一组嵌入式泡沫杯,装有盖子,以限制杯中液体与周围空气之间的热交换(见图 )。在典型的热量测量实验中,特定数量的反应剂被分放在不同的容器中,每个反应剂的温度被测量。然后它们混入开始反应的热量计中。反应混合物在反应完成之前会起动,反应温度会不断受到监测。

A simple constant-pressure calorimeter.
::简单的常压卡路里计。

The key to all calorimetry experiments is the assumption that there is no heat exchange between the insulated calorimeter and the room. Consider the case of a reaction taking place between aqueous reactants. The water in which the solids have been dissolved is the surroundings, while the dissolved substances are the system. The temperature change that is measured is the temperature change that is occurring in the surroundings. If the temperature of the water increases as the reaction occurs, the reaction is exothermic . Heat was released by the system into the surrounding water. An endothermic reaction absorbs heat from the surroundings, so the temperature of the water decreases as heat leaves the surroundings to enter the system.
::所有热量测定实验的关键是假设隔热热热热量计与房间之间没有热交换。考虑水反应器之间发生反应的情况。固态溶解的水是周围, 而溶解的物质是系统。测量的温度变化是周围正在发生的温度变化。如果反应发生时水温度上升, 反应是异温的。系统将热释放到周围的水中。一种内温反应吸收周围的热, 因此当热离开周围进入系统时, 水的温度会下降。

The temperature change of the water is measured in the experiment and the specific heat of water can be used to calculate the heat absorbed by the surroundings $\begin{align*}(q_{\text{surr}})\end{align*}$ .
::实验中测量了水的温度变化,可使用特定的热量计算周围(qsurr)吸收的热量。

$\begin{aligned} q_{surr} = m \times c_{p} \times Δ T \end{aligned}$
$\begin{align*}q_{\text{surr}}=m \times c_p \times \Delta T\end{align*}$
::Qsurr=mxcpT

In the equation, $\begin{align*}m\end{align*}$ is the mass of the water, $\begin{align*}c_p\end{align*}$ is the specific heat of the water, and $\begin{align*}\Delta T\end{align*}$ is $\begin{align*}T_f - T_i\end{align*}$ . The heat absorbed by the surroundings is equal, but opposite in sign, to the heat released by the system. Because the heat change is determined at constant pressure , the heat released by the system $\begin{align*}(q_{\text{sys}})\end{align*}$ is equal to the change $\begin{align*}(\Delta H)\end{align*}$ .
::在等式中, m 是水的质量, cp 是水的具体热量, cp 是 T-T。周围吸收的热量与系统释放的热量相等, 但与系统释放的热量正好相反。由于热量变化是由恒定压力决定的, 系统释放的热量( qsys) 等于变化 ( H) 。

$\begin{aligned} q_{sys} = Δ H = - q_{surr} = - (m \times c_{p} \times Δ T) \end{aligned}$
$\begin{align*}q_{\text{sys}}=\Delta H=-q_{\text{surr}}=-(m \times c_p \times \Delta T)\end{align*}$
::QsysHqsurr(mxcpT)

The sign of $\begin{align*}\Delta H\end{align*}$ is positive for an endothermic reaction and negative for an .
::@HH的征兆对局部热反应是积极的,

Sample Problem: Calorimetry and Enthalpy Changes
::样本问题: 量度测量和酶变化

In an experiment, 25.0 mL of 1.00 M HCl at 25.0°C is added to 25.0 mL of 1.00 M NaOH at 25.0°C in a foam cup calorimeter. A reaction occurs and the temperature rises to 32.0°C. Calculate the enthalpy change $\begin{align*}(\Delta H)\end{align*}$ in kJ for this reaction. Assume the densities of the solutions are 1.00 g/mL and that their specific heat is the same as that of water.
::在一次实验中,在25.0°C的泡沫杯卡路里,在25.0°C的25.0毫升(MHl)加上25.0毫升(MOH),在25.0°C的25.00毫升(MOH),反应发生,温度上升至32.0°C。计算KJ这种反应的蚂蚁变化。假定溶液的密度为1.00克/毫升(mL),其特定热量与水相同。

Step 1: List the known quantities and plan the problem .
::第1步:列出已知数量并规划问题。

Known
::已知已知

$\begin{align*}c_p= 4.18 \text{ J/g}^\circ \text{C}\end{align*}$
::cp=4.18 J/g______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{align*}V_{\text{final}}= 25.0 \text{ mL} + 25.0 \text{ mL}= 50.0 \text{ mL}\end{align*}$
::Vfinal=25.0毫升+25.0毫升=5.0毫升

$\begin{align*}\Delta T= 32.0^\circ \text{C}-25.0^\circ \text{C}= 7.0^\circ \text{C}\end{align*}$
::T=32.0C-25.0C=7.0C

Density = 1.00 g/mL
::密度=1.00克/毫升

Unknown
::未知

$\begin{align*}\Delta H= ? \text{ kJ}\end{align*}$
::H=KJ吗?

The volume and density can be used to find the mass of the solution after mixing. Then calculate the change in enthalpy by using $\begin{align*}\Delta H = q_{\text{sys}}= -q_{\text{surr}}= -(m \times cp \times \Delta T)\end{align*}$ .
::容量和密度可以用来在混合后找到溶液的质量。然后使用 @H=qsysqsurr(mxcpT)计算 enthalpy 的变化。

Step 2: Solve .
::步骤2:解决。

$\begin{aligned} m & = 50.0 ml \times \frac{1.00 g}{mL} = 50.0 g \\ Δ H & = - (m \times c_{p} \times Δ T) = - (50.0 g \times 4.18 {J/g}^{\circ} C \times {7.0}^{\circ} C) = - 1463 J = - 1.5 kJ \end{aligned}$
$\begin{align*}m&=50.0 \text{ ml} \times \frac{1.00 \text{ g}}{\text{mL}}=50.0 \text{ g} \\ \Delta H &=-(m \times c_p \times \Delta T)=-(50.0 \text{ g} \times 4.18 \text{ J/g}^\circ \text{C} \times 7.0^\circ \text{C})=-1463 \text{ J}=-1.5 \text{ kJ}\end{align*}$
::m=50.0 ml×1.00 gmL=50.0 gH(m×cpT)(50.0 g×4.18 J/gC×7.0C)14663 J1.5 kJ

Step 3: Think about the result .
::步骤3:考虑一下结果。

The enthalpy change is negative because the reaction releases heat to the surroundings, resulting in an increase in temperature of the water.
::变化为负值,因为反应向周围释放热量,导致水温上升。

Summary
::摘要

The process of calorimetry is described.
::介绍了热量测定过程。

Calculations involving enthalpy changes are illustrated.
::说明涉及变化的计算。

Review
::回顾

What kinds of reactions are usually analyzed in a calorimeter?
::哪些反应通常在卡路里计中分析?

What is a constant-pressure calorimeter?
::什么是常压卡路里计?

Why are foam cups used in a calorimeter?
::为什么泡沫杯用在热量计上?

Section outline

General

量度测量

How many calories are in your food? ::你的食物里有多少卡路里?

Calorimetry ::量度测量

Sample Problem: Calorimetry and Enthalpy Changes ::样本问题: 量度测量和酶变化

Summary ::摘要

Review ::回顾

How many calories are in your food?
::你的食物里有多少卡路里?

Calorimetry
::量度测量

Sample Problem: Calorimetry and Enthalpy Changes
::样本问题: 量度测量和酶变化

Summary
::摘要

Review
::回顾